Chapter 13 – Surface Areas and Volumes

A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm. Such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius to the [...]

A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 1.5 cm and height 4 cm. How many bottles are needed to empty the bowl? A heap of rice is in the form of a cone of diameter 9 m [...]

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 4119/21 m^3 of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building? A building is in the form of a cylinder surmounted by a hemispherical [...]

A rocket is in the form of a right circular cylinder closed at the lower end and surmounted by a cone with the same radius as that of the cylinder. The diameter and height of the cylinder are 6 cm and 12 cm, respectively. If the slant height of the conical portion is 5 cm, [...]

A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap. A cylindrical bucket of height [...]

A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm, respectively. Find the cost of milk at the rate of Rs 22 per L which the container can hold. A [...]

16 glass spheres each of radius 2 cm are packed into a cuboidal box of internal dimensions 16 cm x 8 cm x 8 cm and then the box is filled with water. Find the volume of water filled in the box. 16 glass spheres each of radius 2 cm are packed into a cuboidal [...]

500 persons are taking a dip into a cuboidal pond which is 80 m long and 50 m broad. What is the rise of water level in the pond, if the average displacement of the water by a person is 0.04 m^3? 500 persons are taking a dip into a cuboidal pond which is 80 [...]

A solid iron cuboidal block of dimensions 4.4 m x 2.6m x 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe. A solid iron cuboidal block of dimensions 4.4 m x 2.6m x 1m is recast into a hollow cylindrical pipe [...]

Water is flowing at the rate of 15 kmh^-1 through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in pond rise by 21 cm? Water is flowing at the rate of 15 kmh^-1 through a pipe [...]