M L Aggarwal Solutions for Chapter: Surface Areas and Volumes, Exercise 2: Exercise 14.2

The largest possible sphere is carved out of wooden solid cube of side $7 \mathrm{cm}$. Find the volume of the wood left.

From a cube of edge $14 \mathrm{cm}$, a cone of maximum size is carved out. Find the volume of the remaining material.

A cone of maximum volume is carved out of a block of wood of size$20 \mathrm{cm}\times 10 \mathrm{cm}\times 10 \mathrm{cm}$. Find the volume of the remaing wood.

From solid cube of side $7 \mathrm{cm}$, a conical cavity of height $7 \mathrm{cm}$ and radius $3 \mathrm{cm}$ is hollowed out. Find the volume of the remaining solid.

$16$ glass spheres each of radius $2 \mathrm{cm}$ are packed in a cuboidal box of internal dimensions $16 \mathrm{cm}\times 8\mathrm{cm}\times 8\mathrm{cm}$ and then the box is filled with water. Find the volume of the water filled in the box.

A heap of rice is in the form of a cone of base diameter $24 \mathrm{m}$ and height $3.5 \mathrm{m}$. Find the volume of the rice. How much canvas cloth is required to just cover the heap?

 A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains $41\frac{19}{21} {\mathrm{m}}^3$ of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the building ? 

A 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 $6 \mathrm{cm}$ and $12 \mathrm{cm}$, respectively. If the slant height of the conical portion is $5 \mathrm{cm}$ then find the total surface area and volume of the rocket. ·