R S Aggarwal and Veena Aggarwal Solutions for Exercise 5: MULTIPLE-CHOICE QUESTIONS (MCQ)

A sphere of diameter $12.6\mathrm{cm}$ is melted and cast into a right circular cone of height $25.2\mathrm{cm}.$ The radius of the base of the cone is

A spherical ball of radius $3\mathrm{cm}$ is melted and recast into three spherical balls. The radii of two of these balls are $1.5\mathrm{cm}$ and $2\mathrm{cm}.$ The radius of the third ball is

The radius of a hemispherical balloon increases from $6\mathrm{cm}$ to $12\mathrm{cm}$ as air is being pumped into it. The ratio of the surface areas of the balloons in two cases is

The volumes of two spheres are in the ratio $64:27$ and the sum of their radii is $7\mathrm{cm}$. The difference in their total surface areas is

A hemispherical bowl of radius $9 \mathrm{cm}$ contains a liquid. This liquid is to be filled into cylindrical small bottles of diameter $3 \mathrm{cm}$ and height $4 \mathrm{cm}$. How many bottles will be needed to empty the bowl?

A cone and a hemisphere have equal bases and equal volumes. The ratio of their heights is

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is

If the volume and the surface area of a sphere are numerically the same then its radius is