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MENSURATION 1. The internal and external diameters of a hollow hemispherical vessel are 42 cm and 45.5 cm, respectively. Find the volume and its outer curved surface area. 2. A tent in the form of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of the cloth required to make the tent at the rate of Rs. 80 per m2. 3. The radii of circular ends of a solid frustum are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area. 4. A tent in the form of a right circular cylinder up to a height of 4 m and base diameter 4.2 m is surmounted by a cone of equal base and height 2.8 m. Find the capacity of the tent and the cost of the canvas required at the rate of Rs.100 per m2 . 5. A right triangle, whose two smaller sides are 15 cm and 20 cm, is made to revolve about its hypotenuse. Find the volume and the surface area of the double cone so formed. ( Use π = 3.14). 6. Find the capacity of a bucket, 45 cm high, the radii of whose two circular ends are 7 cm and 28 cm. 7. A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 7 cm and height 3 cm. Find the number of cones so formed. 8. The curved surface area of a cone is 12320 cm2. If the radius of its base is 56 cm, find its height. 9. The radii of the internal and external surfaces of a solid metallic shell are 3 cm and 5 cm, respectively. It is melted and recast into a cylinder of height 32/3 cm. Find the diameter of the cylinder. 10. Find the volume of a solid in the form of a cylinder with hemispherical ends whose total length is 2.7 m and the diameter of each hemispherical end is 0.7 m. 11. A circus tent is cylindrical up to a height of 3 m and conical above it. If its radius is 52.5 m and slant height of the conical portion is 53 m, find the area of the canvas needed to make the tent. 12. A solid is in the form of a cylinder 2 m long with hemispherical ends each of 2 m diameter. Find its capacity. 13. A well of diameter 2 m is dug 14 m deep. The earth taken out is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment. 14. An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a horizontal table. Inside this is placed a right circular cone of base diameter 3.5 cm and height 8 cm. Find the volume of the water required to fill the vessel 15. A bucket has top and bottom diameters as 40 cm and 20 cm respectively. Find the volume of the bucket, if its depth is 12 cm. Also, find the cost of tin sheet used to make the bucket at the rate of Rs. 1.20 per dm². (Take π = 3.14) 16. The rain water from a roof 22 m x 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. lithe vessel is just full, find the rainfall in cm. Chandan’s Sample Papers : Sure Success and Excellent Marks 17. A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the bucket if the cost of metal sheet used is Rs. 15 per 100 cm2. 18. A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm. If the height of the toy is 12cm, find the number of toys so formed. 19. A bucket is in the form of a frustum of a cone with a capacity of 12308.8 c.cm of water. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of the metal sheet used in its making. 20. A bucket made of aluminium sheet is of circular pipe in half hour height 20 cm and its upper and lower ends are of radius 25 cm and 10 cm respectively. Find the cost of making the bucket if the aluminium sheet costs Rs. 70 per 100 cm2. 21. Water flows out through a circular pipe, whose internal diameter is 2 cm, at the rate of 0.7 m per second into a cylindrical tank. The radius of whose base is 40cm. By how much will the level of water in the cylindrical tank rise in half an hour? 22. tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13-5 m and radius of base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs 80 per sq. m . Ans; (Rs 82,720) 23. The radii of circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area. Ans:(7599-43 cm2) 24. Two pillars of equal height stand on either side of a roadway which is 150 m wide. From a point on the roadway between the pillars, the elevations of the top of the pillars are 60° and 30°. Find the height of the pillars and the position of the point. Ans:(64-88m ) 25. A man on the deck of a ship is 10 m above water level. He observes that the angle of elevation of the top of a hill is 60° and the angle of depression of the base of the hill is 30°. Calculate the distance of the hill from the ship and the height of the hill. ALL THE BEST. Chandan’s Sample Papers : Sure Success and Excellent Marks Chandan’s Sample Papers : Sure Success and Excellent Marks