VIEWS: 2,500 PAGES: 10 CATEGORY: Guides POSTED ON: 2/24/2010
Guide teaches you how to find the area of a circle
Perimeter, Area and Volume Notes Perimeter and circumference are the distance around a figure. The units for perimeter are the same as the given units for a side or radius. Area is the amount of space inside a 2-dimensional plane figure. The units for area are always square units. Given centimeters area square centimeters Given inches area square inches Square centimeters = sq cm = cm 2 Square inches = sq in = in 2 Volume is the amount of space inside a 3-dimensional figure. The units for volume are always cubic units. Given centimeters volume cubic centimeters Given inches volume cubic inches Cubic centimeters = cm 3 Cubic inches = in 3 FINDING PERIMETER To find the perimeter of any polygon find the sum of the lengths of the sides. Examples: 1.) Find the perimeter of the given triangle. Solution: P = 18+26+28 P = 72 centimeters Be sure to include the units (centimeters) 2. Find the perimeter of a hexagon given that each side has a length of 20 inches. Solution: A hexagon has 6 sides. Add all sides together. 20 + 20 + 20 + 20 + 20 + 20 = 120 in or since all the sides are the same length 6(20) = 120 in 3. Find the perimeter of a square with sides of 6 miles. Solution: Since the sides of a square are all equal, the perimeter is 6 + 6 + 6 + 6 = 24 miles or 4(6) = 24 miles 4. Find the perimeter of a rectangle with length 8 inches and width 5 inches. Solution: Sketch the rectangle. Since the opposite side of a rectangle are , we know the lengths of the other sides of the rectangle. We can add all four sides: 8 + 5 + 8 + 5 = 26 inches or since the sides are , 2*l + 2*w = 2(8) + 2(5) = 16+10 = 26 in. The perimeter of a circle is called circumference. C = d or C=2 r. Since you are not using a calculator we will leave the answer in terms of . Examples: 1. Find the circumference of a circle with a radius 12 inches. Solution: r = 12 C = 2 r C = 2 (12) C = 24 inches. 2. Find the circumference of a bike wheel whose diameter is 16 inches. Solution: C= d C = (16) C = 16 inches. Or If the diameter is 16, the radius is 8 inches. (The radius is ½ of the diameter). Now use the formula C = 2 r. C = 2 (8) C = 16 inches. 3. Find the circumference of a pool with radius 25 ft. Solution: C = 2 r C = 2 (25) C = 50 feet. FINDING AREA Examples: 1) Find the area of a triangle with height 8cm and base 12cm. 1 1 Solution: Area = * base * height = * b * h 2 2 1 A= * 8 * 12 2 A = 48 cm 2 or 48 square centimeters. 2) Find the area of a rectangle with length 15 cm and width 10cm. Solution: Area = length * width = l * w. A =15 * 10 A = 150 cm 2 3) Find the area of the given triangle. Solution: In a right triangle, the base and height are the two perpendicular legs. 1 A= b*h 2 1 = *6*8 2 = 3*8 =24 in 2 4) Find the area of the parallelogram. Solution: Area of a parallelogram = base * height A = b*h = 25 * 10 = 250 in 2 (The 12 is a side. The height and base are always to each other.) 5) Find the area of a circle with a radius 6m. Solution: A = r2 A = (6) 2 A = 36 m 2 6) Find the area of a circle with diameter 20 in. Solution: We need the radius for the area formula. A= r 2 , r = 10 A = (10) 2 A = (100) A = 100 in 2 7) Find the area of the shaded region. Solution: Find the area of the large rectangle minus the area of the small rectangle. A L = 6*8 A s = 2*4 A Shaded = 48-8 2 2 = 48 m =8m = 40 m 2 8) Find the area of the shaded region. Solution: Find the area of the large circle minus the area of the small circle. AL = r2 As= r2 A Shaded = 36 - 16 = 62 = (4) 2 = 20 cm 2 = * 36 = * 16 = 36 cm 2 = 16 cm 2 FINDING VOLUME Examples: 1) Find the volume of a box with length 8in, width 10in, and height 10in. Solution: V=l*w*h = 8 * 10 * 10 = 80 * 10 = 800 in 3 2) A fish tank is 20in long, 15in wide, and 15in high. How much water does the tank hold (one gallon = 231 in 3 )? Solution: V = l*w*h = 20 * 15 * 15 = 300 * 15 in 3 = 4,500in 3 1 gallon x gallons Use a proportion: 3 = 231in 4500in3 Cross multiply: 4500 * 1 = 231x 4500 = 231x x 19.5 3) Find the volume of a cylinder with radius 4ft and height 5ft. Solution: V= r 2 h V (4) 2 (5) V *16*5 V *80 V 80 ft 3 4) Find the volume of a can that is 6 inches tall and has a diameter of 10 inches. Solution: V r 2 h d =10 inches-----------------r = 5 inches (5) (6) 2 V V *25*6 V *150 V 150 in3 5) Find the volume of a ball with radius 3cm. 4 Solution: Volume of a sphere = V= r3 3 4 V = (3)3 3 4 V = *27 3 Cross cancel 4 9 V= 27 13 V = 4 *9 V = 36 cm3 6) Find the volume of a cube with length of a side 3ft. Solution: (edge = e) V = e3 V = 33 or 3 * 3 * 3 V = 27 ft 3 Practice Perimeter, Area and Volume Directions: Find the perimeter, area or volume. Pay special attention to units. 1. Find the perimeter of a square with side 7in. 2. Find the area of a square with side 9in. 3. Find the area of 4. Find the area of 5. Find the area of a circle with diameter 14in. 6. Find the volume of a can with height of 9ft and diameter 10ft. 7. Find the volume of a ball with diameter10m. 8. Find how much fence is needed to go around a lot that is 1000 feet by 800 feet. 9. Find how much tile is needed to cover a room 30 by 60 . 10. A roll of aluminum foil is 12 inches wide and 75 feet long. Find the area of the roll of aluminum. See answers below. Answers to Practice. 1. P = 7*4 = 28 inches 2. A = 9 2 or 9 * 9 = 81 in 2 3. A = 9 * 4 = 36 in 2 1 4. A = * 20 * 8 = 10 *8 = 80 in 2 2 5. d = 14, r = 7, A= r 2 (7) 2 * 49 49 cm2 = 153.86 cm2 6. r = 5, V r 2 h (5) 2 (9) * 25*9 225 ft 3 = 706.5 ft3 4 3 4 4 4000 7. V = r (10)3 (1000) m3 = 4,186.7 m3 (rounded to tenths place) 3 3 3 3 8. P = 2l+2w=2(1000) + 2(800) = 2000 + 1600 = 3600ft or 1000 + 1000 + 800 + 800 = 3600ft 9. A = l * w = 30 * 60 = 1800sq ft. 10. ** Caution the units are different. Change 12in = 1ft A = l * w = 75 * 1 = 75 sq ft.