M L Aggarwal Solutions for Exercise 7: Chapter Test

A cylinder of maximum volume is cut out from a wooden cuboid of length $30 \mathrm{cm}$ and cross-section a square of side $14 \mathrm{cm}$. Find the volume of the cylinder and the volume of wood wasted. [Use $\mathrm{\pi }=\frac{22}{7}$]

Find the volume and the total surface area of a cone having slant height $17 \mathrm{cm}$ and base diameter $30 \mathrm{cm}$. Take $\pi =3.14$.

The volume of hemisphere is $2425\frac{1}{2} {\mathrm{cm}}^3$. Find its curved surface area.

A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is $4.2 \mathrm{cm}$ and the total height of the toy is $10.2 \mathrm{cm}$, find the volume of the toy. (Use $\mathrm{\pi }=\frac{22}{7}$)

A cone and a cylinder are of the same height. If diameters of their bases are in the ratio $3:2$, find the ratio of their volumes.

A solid cone of base radius $9 \mathrm{cm}$ and height $10 \mathrm{cm}$ is lowered into a cylindrical jar of radius $10 \mathrm{cm}$, which contains water sufficient to submerge the cone completely. Find the rise in water level in the jar.

The entire surface of a solid cone of base radius $3 \mathrm{cm}$ and height $4 \mathrm{cm}$ is equal to the entire surface of a solid right circular cylinder of diameter $4 \mathrm{cm}$. Find the ratio of their volumes.

Find the least number of coins of diameter $2.5 \mathrm{cm}$ and height $3 \mathrm{mm}$ which are to be melted to form a solid cylinder of radius $3 \mathrm{cm}$ and height $5 \mathrm{cm}$.