Chapter 14 - Mensuration

Exercise - 28

1. A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1cm and the height of the cone is 4cm. The solid is placed in a cylindrical tub, full of water, in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5cm and its height is 9.8cm, find the volume of the water left in the cylindrical tub.
2. A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2cm and the total height of the toy is 10.2cm, find the volume of the wooden toy.
3. A toy is in the form of a cone mounted on a hemisphere of radius 7cm. The total height of the toy is 14.5cm. Find the volume and the total surface area of the toy..
4. A toy is in the form of a cone mounted on a hemisphere of radius 3.5cm. The total height of the toy is 15.5cm. Find the total surface area and the volume of the toy.
5. A building is in the form of a hemispherical vaulted done and contains of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.
6. A circus tent is in the shape of a cylinder surmounted by a cone. The diameter of the cylindrical part is 24m and its height is 11m. If the vertex of the tent is 16m above the ground, find the area of canvas required to make the tent.
7. An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8cm. The cylindrical part is 240cm high and the conical part is 36cm light. Find the weight of the pillar if one cu.cm of iron weight 7.8 grams.
8. A circus tent is made of canvas and is in the form of a right circular cylinder and a right circular cone above it. The diameter and height of the cylindrical part of the tent are 176m and 5m respectively. The total height of the tent is 21m. Find the total cost of the tent if the canvas used costs Rs. 12 per square meter.
9. A circus tent has cylindrical shape surmounted by a conical roof. The radius of the cylindrical base is 20m. The height of cylindrical and conical portions are 4.2m and 2.1m respectively. Find the volume of tent.
10. A petrol tank is a cylinder of base diameter 21cm and 18cm length fitted with conical ends each of axis length 9cm. determine the capacity of the tank.

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