From a 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.

Two cones same base radius $8 \mathrm{cm}$ and height $15 \mathrm{cm}$ are joined together along their bases. Find the surface area of the shape so formed.

Two solid cones $A$ and $B$ are placed in a  cylindrical tube as shown in the figure. The ratio of their capacities is $2:1$. Find the heights and capacity of cones. Also, find the volume of the remaining portion of the cylinder.

An ice-cream cone full of ice - cream having radius $5 \mathrm{cm}$ height $10 \mathrm{cm}$ as shown in figure

Calculate the volume of ice-cream, provided its $\frac{1}{6}$ part is left unfilled with ice-cream.

Marbles of diameter $1.4 \mathrm{cm}$ are dropped into a cylindrical beaker of diameter $7 \mathrm{cm}$ containing some water. Find the number of marbles that should be dropped into the beaker, so that the water level rises by $5.6 \mathrm{cm}$. 

How many spherical lead shots each of diameter $4.2 \mathrm{cm}$ can be obtained from a solid rectangular lead piece with dimensions $66 \mathrm{cm}, 42 \mathrm{cm}$ and $21 \mathrm{cm}$ ?

How many spherical lead shots of diameter $4 \mathrm{cm}$ can be made out of a solid cube of lead whose edge measures $44 \mathrm{cm}$.

A wall $24 \mathrm{m}$ long $0.4 \mathrm{m}$ thick and $6 \mathrm{m}$ high is constructed with the bricks each of dimensions $25 \mathrm{cm}\times 16 \mathrm{cm}\times 10 \mathrm{cm}$. If the mortar occupies $\frac{1}{10}$th of the volume of the wall, then find number of bricks used in constructing the wall.

Find the number of metallic circular disc with $1.5 cm$ base diameter and of height $0.2 cm$ to be melted to form a right circular cylinder of height $10 cm$ and diameter $4.5 cm$.