NCERT Solutions for Chapter: Surface Areas and Volumes, Exercise 4: Exercise

A cylindrical tube opened at both the ends is made of iron sheet which is $2 \mathrm{cm}$ thick. If the outer diameter is $16 \mathrm{cm}$ and its length is $100 \mathrm{cm},$ find how many ${\mathrm{cm}}^3$ of iron has been used in making the tube?

A semicircular sheet of metal of diameter $28 \mathrm{cm}$ is bent into a form of open conical cup. The capacity of the cup$=$_____${\mathrm{cm}}^3$.

A cloth having an area of $165 {\mathrm{m}}^2$ is shaped into the form of a conical tent of radius $5 \mathrm{m}$

(i) How many students can sit in the tent if a student, on a average occupies $\frac{5}{7} {\mathrm{m}}^2$ on the ground?

(ii) Find the volume of the cone.

The water for a factory is stored in a hemispherical tank whose internal diameter is $14 \mathrm{m}$. The tank contains $50$ $kilolitres$of water. Water is pumped into the tank to fill to its capacity. Calculate the volume of water pumped into the tank.

The volumes of the two spheres are in the ratio $64 : 27 .$ Find the ratio of their surface areas.

A cube of side $4 \mathrm{cm}$ contains a sphere touching its sides. Find the volume of the gap in between.

A sphere and a right circular cylinder of the same radius have equal volumes. By what percentage does the diameter of the cylinder exceeds its height?

$30$ circular plates, each of radius $14 \mathrm{cm}$ and thickness $3 \mathrm{cm}$ are placed one above the another to form a cylindrical solid. Find
(i) the total surface area.
(ii) volume of the cylinder so formed.