MULTIPLE CHOICE QUESTIONS
1. In below figure area of ABC 100 and area of PQR 225 . What is the value of r ' if r 8cm ?
a. 8 cm b. 12 cm c. 18 cm d. 4 cm Sol: Correct option is (b)
Here ratio of sides =
225 1.5 100
r ' 1.5 r 1.5 8 12cm
2. The measure of angles of a quadrilateral taken in order are proportional to 1:2:4:5, then the quadrilateral is
a. parallelogram b. square c. trapezium d. none of the above Sol: Correct option is (c)
Let the angles be x, 2 x, 4 x, 5 x
x 2 x 4 x 5 x 360 12 x 360 x 30
Angles are 30, 60, 120, and 150
As SR II PQ PQRS is a trapezium 3. Find the measure of the smallest angle of a quadrilateral if the measures of its interior angles are in the ratio 2:3:3:4? a. 60 o b. 120o c. 90o d. 180o Sol: Correct option is (a)
Let the angles be 2 x,3 x, 3 x, 4 x
2 x 3 x 3 x 4 x 360 12 x 360 x 30
Smallest angles = 2 x 60 o
4. In below figure PQRS is a parallelogram. Also PQ= 8 cm and PS = 6 cm. What is the area of this parallelogram?
a. 12cm 2 b. 48cm 2 c. 24cm 2 d. 8cm 2 Sol: Correct option is (c)
Area = PQ ST Here PQ = 8 cm and
ST 1 sin 30o ST 6 3cm PS 2
Area = 8 3 24cm 2 5. In below figure PQRS is a rhombus with each side 5 cm. What is the length of diagonal PR if SR = 8 cm
a. 6 cm b. 5 cm c. 8 cm d. 2 cm Sol: Correct option is (a)
Here PQ= 5 cm
1 Also OQ= SQ 4cm 2
PO PQ 2 OQ 2 52 42 3 PQ 2 3 6cm
6. In below figure PQRS is a parallelogram PO and OQ are bisectors of P and Q . What is the measure of POQ ?
a. 60 o b. 30o c. 90o d. 45 o Sol: Here Correct option is (c)
1 1 P Q POQ 180o 2 2
1 (P Q ) POQ 180o 2 1 (180o ) POQ 180o 2
POQ 90o
7. What is the value of x in below figure if PQRS is a parallelogram
a. 60 o b. 30o c. 70 o d. 75o Sol: Correct option is (d)
SRQ SPQ 60o 45o 60o x 180o x 180o 45o 60o x 75o
8. Two parallelogram stand on same base and between the same parallel lines. What is the ratio of their areas? a. 1:2 b. 1:3 c. 2:5 d. 1:1 Sol: Correct option is (d)
As both have same base and also same height, therefore they have equal area and hence ration = 1:1
9. In below figure PQRS is a parallelogram and STUR is a rectangle. Which of the following statement is true?
a. perimeter of PQRS < perimeter of STUR b. perimeter of PQRS > perimeter of STUR c. perimeter of PQRS = perimeter of STUR d. none of the above Sol: Correct option is (b)
Perimeter of PQRS = 2 (SR+PS) Perimeter of STUR = 2 (SR+ST) We know that in PTS PS >ST as PS is hypotenuse
Perimeter of PQRS > Perimeter of STUR
10. For a regular polygon having n sides. What is the sum of all interior angles? a. (n 4) 180 b. (n 2) 180 c. ( n 2) 90 d. (n 3) 90 Sol: Correct option is (b)
Sum of all interior angles = (n 2) 180 For triangles n 3 sum= (3 2) 180 180 o For quadrilateral n 4 sum= (4 2) 180 360o 11. What is the number of sides in a regular polygon if its exterior angle is x ? a. 360 x b.
x 360 360 x
c.
d.
180 x
Sol:
Correct option is (c)
3 6 0 3 6 0 E x te r io r x a n g le
Number of sides =
12. What is the number of diagonals in the regular polygon having n sides? a.
n( n 3) 2 n( n 3) 4 n(n 2) 3
b.
c.
d. n( n 1) Sol: Correct option is (a)
Number of diagonals = nC2 n
n! n(n 1) n 2 3n n(n 3) n n (n 2)!2! 2 2 2
13. What is the area of polygon having n sides and length of each side as x ? a.
nx 180 tan 2 n
360 b. nx 2 tan n
c.
nx 2 360 sin 4 n
nx 2 180 cot 4 n
Correct option is (d)
d.
Sol:
Area of regular polygon having n sides and length of each side as x = nx 2 180 cot 4 n For example Area of equilateral triangle having length of each side x is =
3x 2 3x 2 1 3x 2 cot 60o 4 4 4 3
14. Each interior angle of a regular polygon is 120 o . What is the number of sides of the polygon? a. 2 b. 7 c. 8 d. 6 Sol: Correct option is (d)
Interior angle = 120o
Exterior angle = 180 o 120 o 60o Number of sides =
360o 6 60o
15. Each angle of a regular octagon is a. 150 o b. 135o c. 120 o d. 90o Sol: Correct option is (b)
In octagon number of sides = 8
Exterior angle =
360 45o 8
Interior angle = 135 o
16. The sum of all interior angles of a polygon is 900o . The number of sides of the polygon is a. 5 b. 6 c. 7 d. 8 Sol: Correct option is (c)
Here sum of all interior angles = 900o
(n 2) 180 900 n 900 2 180
n7 17. If each interior angle of a regular polygon is 9
8 times of one of the
interior angles of a regular hexagon, then the number of sides of the polygon is a. 4 b. 6 c. 5 d. 8 Sol: Correct option is (d)
Interior angle of regular hexagon = 120o
Interior angle of regular polygon =
Exterior angle of polygon = 45 o 360o Number of sides = 8 45o
9 120 135o 8
18. If each interior angle of a regular polygon is double its exterior angle, then the number of sides of the polygon is a. 6 b. 4 c. 8 d. 12 Sol: Correct option is (a)
Here Interior angle = 2 Exterior angle
We know that interior angle = 180 360 360 2 n n 360 n
360 360 and exterior angle = n n
180
180 3
n
3 360 6 180
19. The interior angle of a regular polygon is 90o more than its exterior angle. What are the numbers of sides of a regular polygon? a. 4 b. 6 c. 8 d. 10 Sol: Correct option is (c)
360 360 and exterior angle = n n
Interior angle = 180 180
360 360 90o n n
2
360 90o n 2 360 8 90
n
20. What are the numbers of diagonals of a regular polygon having 7 sides?
a. 10 b. 12 c. 11 d. 14 Sol: Correct option is (d)
n( n 3) 2 7(7 3) 7 4 14 2 2
Number of diagonals of polygon of n sides =
Number of diagonals of regular polygon of 7 sides =
21. A regular polygon has 27 diagonals. What are the number of sides of this regular polygon has? a. 9 b. 6 c. 7 d. 10 Sol: Correct option is (a)
n( n 3) 2
Number of diagonals of regular polygon of n sides = n(n 3) 27 2
n(n 3) 54 n 2 3n 54 0 (n 9)(n 6) 0 n9
22. The sum of the number of sides of two regular polygons is 14. The difference between the interior angles of two polygon is 15o . What are the number of sides the two polygons have? a. 4, 6 b. 6, 9 c. 6, 8 d. 8, 11 Sol: Correct option is (c)
Let n and n ' be the number of sides of 2 polygons
n n ' 14
360 360 Also 180 180 ' 15 n n
360 360 15 n' n
Also n ' 14 n
360 360 15 n 8 14 n n
n ' 14 8 6
Hence the number of sides are 6, 8 23. The sum of all interior angles of a regular polygon exceeds the sum of all exterior angles by 180 o . What are the number or sides this polygon has? a. 4 b. 5 c. 6 d. 8 Sol: Correct option is (b)
Sum of exterior angles = 360o Sum of interior angles = 360 o 180 o 540 o
(n 2) 180 540 n2 3 n5
24. The sum of all interior angles of a regular polygon is 3 times the sum of all exterior angle. What are the number of side this polygon has? a. 8 b. 4 c. 6 d. 7 Sol: Correct option is (a)
Sum of exterior angles = 360o Sum of interior angles = 3 360 o 1080o
(n 2) 180 1080 n26 n 8
25. What is the ratio of the measure of interior angle to the measure of exterior angle of a regular hexagon? a. 1:4 b. 3:1 c. 2:3 d. 2:1 Sol: Correct option is (d)
Here n 6
Exterior angle =
360 60o 6
Interior angle = 180 o 60o 120o Ratio =
120 2 :1 60
26. A regular polygon has 27 diagonals. What is the measure of each interior angle of this regular polygon? a. 120 o b. 108o c. 140o d. 90o Sol: Correct option is (c)
Here number of diagonals = 27 n(n 3) 27 2
n 2 3n 54 0 (n 9)(n 6) 0 n9
Interior angle = 180
360 140 o 9
9 27. The interior angles of a polygon P is times, the interior angle of 4 ' polygon P . What is the ratio of the number of sides of these polygons? Given sum of sides = 11
a. 3:8
b. 7:3 c. 3:4 d. 5:8 Sol: Correct option is (a)
Let polygon P has n sides and polygon P' has n ' sides
180 360 9 360 180 ' 4 n n 360 810 405 ' n n
180
Also n n ' 11 180 360 810 405 n 11 n
n 8 n' 3 n' 3 3:8 n 8 28. Which of the following statement is true for the two congruent circles? a. they have equal radius b. they have equal perimeter c. they have equal area d. all of the above Sol: Correct option is (d)
Congruent circles have equal radius they have equal area and perimeter 29. In below figure PQRS is a quadrilateral inscribed in a circle with centre O. What is the value of x in the below figure?
a. 100 o b. 110 o c. 10o d. 90o Sol: Correct option is (b)
In a cyclic quadrilateral the sum of opposite angles equal to 180 o .
x 70o 180o x 110o
30. In below figure PQ=RS, then which of the statement is true?
a. x 2 y b. x
y 2
c. x y d. xy 1 Sol:
x y
Correct option is (c)
Equal chords of a circle subtend equal angles at the centre 31. What is the value of x in the below figure?
a. 60 o b. 120o c. 90o d. 70 o Sol: Correct option is (b)
Here RSQ 180 QST
RSQ 180 120 60o
Also x RSQ 180o
x 180 RSQ 180 60 x 120o
32. In below figure PS and RQ are two chords intersecting at T. Which of the following is true?
a. PT QT RT TS b. PT TS QT TR c. PS RQ d. PT TS RQ TQ Sol: Correct option is (b)
By the property of intersecting chords PT TS QT TR 33. In below figure PR is secant and PT is tangent to a circle. Which of the following statement is true?
a. PT 2 PR PQ b. PQ 2 PR 2 PT 2 c. PQ 2 QR 2 PT 2 d. PT 2 PR 2 Sol: Correct option is (a)
PT 2 PR PQ
34. Two circles having radii r1 and r2 touch externally. What is the distance between their centres?
a. r12 r2 2 b. r2 r1 c. r1 r2 d. r12 r2 2 Sol: Correct option is (c)
Distance between O and O ' = r1 r2 35. Two circles having radii r1 and r2 touch internally. What is the distance between their centres if r2 r1 ?
a. r1 r2 b. r2 2 r12 c. r12 r2 2 d. r2 r1 Sol: Correct option is (d)
Distance between O and O ' = r2 r1 36. In below figure SR PQ . What is the length of PQ?
a. 18 cm b. 7 cm c. 12 cm d. 5 cm Sol: Correct option is (a)
Here PSR QSR
PR RQ PQ 2 PR
Also PR 152 122 81 9cm
PQ 2 PR 2 9 18cm
37. What is the length of the perpendicular from the centre of a circle having radius 13 cm to the chord of a circle 10 cm long?
a. 5 cm b. 13 cm c. 12 cm d. 10 cm Sol: Correct option is (c)
Here PO= 13 cm and PQ=10 cm Also OR PQ PR
1 PQ 5cm 2
OR PO2 PR 2 132 52 12cm
38. The radius of a circle makes an angle of 50o with a chord of circle. What is the angle subtended by this chord at centre?
a. 70 o b. 50o c. 45 o d. 80o Sol: Correct option is (d)
Here OPQ OQP 50o
POQ 180 50 80o
39. In below figure RPQ 30o and PQR 100o . What is the value of x in below figure?
a. 40 o
b. 100 o c. 50o d. 30o Sol: Correct option is (c)
Here PRQ 180 100 30 50o Also x PRQ 50o
x 50o
40. In below figure, what is the value of x if POR 100o ? a. 120 o b. 130o c. 100 o d. 110 o
Sol:
Correct option is (b)
1 Here PSR POR 2
1 PSR 100 50o 2
Also x PSR 180o
x 180 o 50 o 130 o
41. In below figure O is the centre. What is the value of x in below figure?
a. 40 o b. 90o c. 150 o d. 50o Sol: Correct option is (d)
Here PQR 90o
x 180 90 40 50 o
42. A tangent of 3 cm is drawn to a circle from a point which is 5 cm from the centre of a circle. What is the radius of a circle?
a. 3 cm b. 5 cm c. 4 cm d. 8 cm Sol: Correct option is (c)
Here OP= 5 cm and PQ = 3 cm
OQ 52 32 16 4cm
Radius 4cm 43. In below figure PS = 12 cm and PQ = 4 cm. What is the value of QR?
a. 4 cm b. 12 cm c. 48 cm d. 32 cm Sol: Correct option is (d)
Here PS 2 PQ PQR
PR
PS 2 144 36cm PQ 4
RQ 36 4 32cm
44. In below figure SPR 45o . What is the value of x in below figure? a. 60 o b. 45 o c. 90o d. 30o
Sol:
Correct option is (b)
Here PQR SPR 45o Also RPQ 90o
x 180 90 45 45o
45. In below figure PT = 4 cm, TR = 7 cm and TQ = 2 cm. What is the value of ST?
a. 4 cm b. 8 cm c. 7 cm d. 14 cm Sol: Correct option is (d)
Here ST TQ PT TR ST PT TR 4 7 14cm TQ 2
46. In below figure PQ = 3 cm, QT = 12 cm, PR = 5 cm. What is the value of RS?
a. 4 cm b. 5 cm c. 3 cm d. 1 cm Sol: Correct option is (a) Here PQ PT PR PS
3 15 5 PS PS 9cm RS 9 5 4cm
47. In below figure PQ = 4 cm, and PR = 2 cm. What is the value of RS?
a. 3 cm b. 4 cm c. 6 cm d. 8 cm Sol: Correct option is (c)
Here PQ 2 PR PS
PS
4 4 8cm 2
RS 8 2 6cm
48. Two circles of radii 8 cm and 11 cm touch each other externally. What is the distance between the centres of the two circles?
a. 8 cm b. 11 cm c. 3 cm d. 19 cm Sol: Correct option is (d)
Distance between O and O ' = 11+8= 19 cm 49. Two circles of radii 8 cm and 11 cm touch each other internally. What is the distance between the centres of the two circles?
a. 8 cm b. 3 cm c. 11 cm d. 19 cm Sol: Correct option is (b)
In above figure Distance between O and O ' = r2 r1 =11-8 = 3 cm 60. Three circles touch each other externally. The distance between their centres is 4 cm, 6 cm and 8 cm. What are the radii of the circles?
a. 1 cm, 3 cm, 5 cm b. 1 cm, 3 cm, 6 cm c. 1 cm, 2 cm, 4 cm d. 4 cm, 2 cm, 6 cm Sol: Correct option is (a)
PQ = 4, QR = 6 and PR = 8 Here PQ+QR+PR= 2( x y z )
2( x y z ) 4 6 8 x yz 9
Also x z 4
y5
Also z y 6
z 1 x3
Hence radii are (1, 3, 5) 61. A regular polygon having n sides has 2n diagonals. What are the number of sides of this polygon has? a. 4 b. 7 c. 9 d. 11 Sol: Correct option is (b)
n( n 3) 2
Number of diagonals =
n(n 3) 2n 2
n 2 3n 4n n2 7n
n7
62. A rectangular field has its length and breadth in the ration 3:4. What is the area of rectangular field if its perimeter is 28 cm? a. 24cm 2 b. 48cm 2 c. 40cm 2 d. 12cm 2 Sol: Correct option is (b)
4x 3
Let length be x breadth =
4x 7x 2 x 28 2 28 3 3 x6
Breadth = 8 cm and Length = 6 cm
Also Area = 6 8 48cm 2 63. A rectangular playground costs Rs. 18 at Re. 1 per square metre for leveling. What is the length of the playground if the ratio of length and breadth is 1:2?
a. 2 m
b. 1 m c. 3.8 m d. 3 m Sol: Correct option is (d) Breadth = 2x
Let length = x Also Area =
Rs.18 18m 2 2 1Re/ m 2 x x 18m 2
2 x 2 18m 2 x 3m
64. The ratio of the length and breadth of a rectangular playground is 2:3 and its area is 2400 m 2 . How long will it take to walk around the playground at the rate of 2 km/hr? a. 20 min b. 10 min c. 12 min d. 6 min Sol: Correct option is (d)
Let length be 2x and breadth be 3x
2 x 3 x 2400 x 2 400 x 20m
Perimeter = 2(2 20 3 20) 200m
Time =
200 m 1 1 hr 60 6 min 2000m / hr 10 10
65. If the length of the rectangle is doubled and the breadth remains same then what is the percentage change in the area? a. 100% b. 200% c. 50% d. 150% Sol: Correct option is (a)
If length is doubled then area also gets doubled
A' 2 A
Percentage change =
A' A 2A A 100 100 100% A A
66. How many tiles of length 6 cm and breadth 2 cm are required to cover the rectangular wall of length 18 cm and breadth 8 cm? a. 10 b. 12 c. 6 d. 18 Sol: Correct option is (b)
Area of tile = 6 2 12cm 2 Area of wall = 18 8 144cm 2
Number of tiles =
144cm2 12 12cm 2
67. If the area of the square is 144m 2 , then what is the length of the diagonal of the square?
a. 6 2m b. 6m c. 12m d. 12 2m Sol: Correct option is (d)
Area = 144m 2
Side = 144 12m Diagonal = Side 2 12 2m
68. If the length of a diagonal of a square is 8.484 m, then what is the area of the square? a. 36m 2 b. 24m 2 c. 16m 2 d. 25m 2 Sol: Correct option is (a)
Diagonal = 8.484 m Also diagonal = side 2
side 2 8.484 side 6m
Area 6 6 36 m 2
69. If the side of square is increased by 100% then by how much percentage does its area get increased?
a. 100% b. 200% c. 300% d. 50% Sol: Correct option is (c)
Let side be l
Area l l l 2
After increment new side = 2l
AreaA' (2l ) (2l ) 4l 2 Percentage increase =
4l 2 l 2 100 300% l2
70. What is the length of the base of an isosceles triangle whose area is 6m 2 and length of one of equal side is 5 m? a. 6 m b. 8 m c. 4 m d. 12 m Sol: Correct option is (b)
Area = 12m 2 Let QR = 2a
QS a
Also PS 52 a 2
1 1 Area QS PS a 52 a 2 2 2
1 a 52 a 2 6m 2 2 a 52 a 2 12 a 2 (52 a 2 ) 122 25a 2 a 4 144 a 4m Base QR 2a 8m
71. If every side of a triangle is tripled, then the ratio of the new area to the old area is
a. 3:1 b. 1:3 c. 9:1 d. 2:3 Sol: Correct option is (c)
Let a, b, c be sides of triangle Area =
s( s a)(s b)(s c)
Also a 3a ' , b 3b' , c 3c ' s ' 3s
Area A' 3s (3s 3a)(3s 3b)(3s 3c) 9 s ( s a)(s b)(s c )
A' 9 :1 A
72. What is the area of an equilateral triangle whose altitude is 4 3cm long? a. 8 3cm 2 b. 4 3cm 2 c. 16 3cm2 d. 8cm 2 Sol: Correct option is (c)
Here PS =
a2 a
2
2
3a 2
3a 4 3 a 8cm 2
1 8 4 3 16 3cm 2 2
Area
73. The adjacent sides of a parallelogram are 4 cm and 9 cm and the angle between them is 60 o . What is the area of the parallelogram? a. 18 3cm2 b. 36cm 2 c. 18cm 2 d. 36 3cm 2 Sol: Correct option is (c)
Area = 9 4 sin 60 o
9 4 3 2
18 3cm 2
74. Area of a rhombus is 20cm 2 . One of the diagonal of a rhombus exceeds the other diagonal by 3 cm. What is the length of the smaller diagonal? a. 4 cm b. 6 cm c. 8 cm d. 5 cm Sol: Correct option is (d)
Let smaller diagonal = xcm
Larger diagonal = ( x 3)cm
1 Area x( x 3) 2
1 x( x 3) 20 2 x 2 3 x 40 0 ( x 5)( x 8) 0 x 5cm 75. The length of two parallel sides of a trapezium are 8 cm and 14 cm. What is the area of this trapezium if distance between the parallel lines is 7 cm? a. 11cm 2 b. 77cm 2 c. 144cm 2 d. 154cm 2 Sol: Correct option is (b)
1 (8 14) 7 2
Area of trapezium =
1 (22) 7 77cm 2 2
76. If the circumference of the circle is 14 cm , then what is the area of this circle? a. 49 cm 2 b. 7 cm 2 c. 49cm 2 d. 7cm2
Sol:
Correct option is (a)
Circumference = 2 r 14 r 7cm
Area r 2 (7) 2 49 cm 2
77. The sum of the radius and circumference of a circle, is 153cm. What is 22 the area of the circle? ( ) 7 a. 21 cm 2 b. 441cm 2 c. 441 cm 2 d. 21cm 2 Sol: Correct option is (c) Here r 2 r 153cm
44 r 1 153 7 r 21cm Area r 2 (21)2 441 cm 2
78. The radius of a circle is increased by 100%. What is the percentage increase in the area of the circle? a. 100% b. 50% c. 200% d. 300% Sol: Correct option is (d)
Let initial radius = r Then radius after increment = 2r
Let initial area = A = r 2 Incremented Area = (2r ) 2 4 r 2 A' Percentage increase = A' A 4 r 2 r 2 100 100 300% A r2
79. If the circumference of the circle is increased by 200% what is the percentage increase in the area of the circle? a. 400% b. 200% c. 800% d. 100% Sol: Correct option is (c)
Let initial circumference = C = 2 r Incremented circumference = C ' 2 r 6 r
r ' 3r
A' (3r ) 2 9 r 2
Percentage increase =
A' A 9 r 2 r 2 100 100 800% A r2
80. How long will it take to walk around a circle of radius 14 cm at the rate 22 of 4 cm/min? ( ) 7 a. 22 min b. 12 min c. 11 min d. 88 min Sol: Correct option is (a)
Circumference = 2 r
2 22 14 88cm 7
88cm 22 min 4cm / min
Time =
81. A rope is bent in the form a square of side 22 cm. It is cut again and bent 22 in the form a semicircle. The radius of this semicircle is ( ) 7 a. 14 cm b. 7 cm c. 21 cm d. 28 cm Sol: Correct option is (d)
Perimeter of square = 4 22 88cm Circumference of semicircle = r
r 88cm 22 r 88 7
r 28cm
82. What is the lateral surface area of cuboid having length 2 cm, breadth 4 cm and height 3 cm? a. 18cm 2 b. 36cm 2 c. 9cm 2 d. 4cm 2 Sol: Correct option is (b)
Lateral surface area = 2(l b) h
2(2 4)3 36cm2
83. What is the total surface area of cuboid having length 1 cm, breadth 2 cm and height 4 cm? a. 14cm 2 b. 7cm 2 c. 28cm 2 d. 35cm 2 Sol: Correct option is (c) Total surface area = 2(lb bh hl ) 2(1 2 2 4 4 1) 2(2 8 4) 28cm 2 84. The length of the cuboid is 3cm, breadth 2 cm and height 36 cm. What is the length of each cube which will have the same capacity as that of given cuboid? a. 4 cm b. 2 cm c. 8 cm d. 6 cm Sol: Correct option is (d)
Volume of cuboid = 2 36 3 216 Volume of cube= a 3
a 3 216 a 6cm
85. The length, breadth and height of a box are 3 cm, 4 cm, and 6 cm respectively. What is the cost of covering the box fully if the cost of covering is Rs. 4/ cm 2 . a. Rs. 432 b. Rs. 108 c. Rs. 216 d. Rs. 324 Sol: Correct option is (a)
Surface area of box = 2(3 4 4 6 6 3)
2(12 24 18) 108cm 2
Cost = 4 108 Rs.432 86. When each side of a cube is increased by 3 cm, then the volume is increased by 279 cm3 . What is the length of side or original cube? a. 3 cm b. 4 cm c. 7 cm d. 9 cm Sol: Correct option is (b)
Let the length of side of original cube = x Volume of original cube = x 3 Incremented volume = ( x 3)3
( x 3)3 x3 279 x 3 27 9 x ( x 3) x 3 279 9 x 2 27 x 252 0 x 2 3 x 28 0 ( x 4)( x 7) 0 x 4cm
87. A cube having each edge 5 cm is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 5 cm x 5 cm, what is the rise in the water level? a. 25 cm b. 125 cm c. 5 cm d. 2.5 cm Sol: Correct option is (c)
Volume of cube = (5)3 125cm3 Rise =
125 5cm 5 5
88. A rectangular water reservoir is 10 m by 12 m at the base. Water flows into it through a pipe whose cross section is 4 m by 3 m at the rate of 2 m/sec. what is the height to which the water will rise in the reservoir in 10 seconds? a. 1 m b. 3 m c. 2 m d. 1.5 m
Sol:
Correct option is (c)
Volume of water flown = 4 3 2 10 240m3
Height 240 2m 10 12
89. The lateral surface area of a cylinder is 56 cm 2 . What is the volume of cylinder if its height is 7 cm? a. 56 cm3 b. 28 cm 3 c. 16 cm3 d. 112 cm3 Sol: Correct option is (d) Lateral surface area = 2 rh
2 rh 56 rh 28
As h 7cm
r 4m
Volume (4) 2 7 112 cm3
90. The curved surface area of a cylinder is 60 cm 2 and its base radius is 5 cm, then its total surface area is? a. 55cm 2 b. 22cm 2 c. 110cm 2 d. 30cm 2 Sol: Correct option is (c)
Curved surface area = 2 rh
2 rh 60 cm 2 rh 30
As r = 5 cm h 6cm
Total surface area = 2 r ( h r )
2 (5)(6 5) 110 cm2
91. The ratio between the radius and height of cylinder is 2:3. What is the curved surface area of the cylinder if the volume is 96 cm3 ? Sol: Correct option is (a)
Let radius = 2x and height = 3x
Volume (2 x )2 (3x ) 12 x 3 12 x 3 96 x3 8 x2
Radius = 4 cm and Height = 6 cm Surface area = 48 cm 2