M L Aggarwal Solutions for Chapter: Surface Areas and Volumes, Exercise 4: Exercise 13.4

If the number of square centimetres in surface area of a sphere is equal to the number of cubic centimetres in its volume, find the diameter of the sphere.

If the total surface area of a solid hemisphere is $942 {\mathrm{cm}}^2$, find its diametere. (Use $\mathrm{\pi }=3.14$)

A capsule of medicine is in the shape of a sphere of diameter $3.5 \mathrm{mm}$. How much medicine (in ${\mathrm{mm}}^3$) is needed to fill this capsule?

A shopkeeper has one spherical ladoo of radius $5 \mathrm{cm}$. With the same amount of material, how many ladoos of radius $2.5 \mathrm{cm}$ can be made?

The surface area of a solid sphere is $1256 {\mathrm{cm}}^2$. It is cut into two hemispheres. Find the total surface area and volume of a hemisphere. Take $\mathrm{\pi }=3.14$.

The volume of a sphere is equal to two-third of the volume of a cylinder whose height and diameter are equal to the diameter of the sphere.

The volume of the largest right circular cone that can be fitted in a cube whose edge is $2r$ equals the volume of a hemisphere of radius $r$.

A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is $1:2:3$.