R Chandra Solutions for Chapter: Surface Areas and Volumes, Exercise 2: TEST YOUR SKILLS

If the radius of a cylinder is doubled and height is halved, then its curved surface area will be

If the radius of a sphere is doubled, then what is the ratio of the surface area of original sphere to the new sphere?

If the radius of a sphere is doubled then what is the ratio of the volume of original sphere to the new sphere?

The dimensions of a rectangular metallic sheet are $48 \mathrm{c}\mathrm{m}\times 36 \mathrm{c}\mathrm{m}$. From each corner, a square of side $8 \mathrm{c}\mathrm{m}$ is cut off and open box is made from the remaining sheet. Find the volume of the box.

Two right circular cones of equal curved surface areas have slant heights in the ratio of $3:5$. Find the ratio of their radii.

In the cylindrical container, the base radius is $8 \mathrm{c}\mathrm{m}$. If the height of the water level is $20 \mathrm{c}\mathrm{m}$, find the volume of the water in the container. (Take: $\mathrm{\pi }=3.142)$

The dimensions of a hall are $20 \mathrm{m}\times 16 \mathrm{m}$. The sum of the areas of its floor and flat roof is equal to the surface area of its four walls. Find the volume and height of the hall.

A well with $10 \mathrm{m}$ inside diameter is dug $14 \mathrm{m}$ deep. Earth taken out of it is spread all around it to make an embankment of height $4\frac{2}{3} \mathrm{m}$. Find the width of the embankment.