M L Aggarwal Solutions for Exercise 4: EXERCISE 16.4

A closed rectangular wooden box has inner dimensions $90 \mathrm{cm}$ by $80 \mathrm{cm}$ by $70 \mathrm{cm}$. Compute its capacity and the area of the tin foil needed to line its inner surface.

A cube of metal of 6 cm edge is melted and cast into a cuboid whose base is $9 cm \times 8 cm$.Find the height of the cuboid.

Three cubes whose edges are $x \mathrm{cm}$,$8 \mathrm{cm}$ and $10 \mathrm{cm}$ respectively are melted and recast into a single cube of edge $12 \mathrm{cm}$. Find $x$.

The area of cross-section of a pipe is $3.5 {\mathrm{cm}}^2$ and water is flowing out of pipe at the rate of $40 \mathrm{cm}/\mathrm{s}$. How much water is delivered by the pipe in one minute?

The figure given below shows a solid of uniform cross-section. Find the volume of the solid. All measurements are in cm and all angles in the figure are right angles.

The figure given below shows the cross-section of a concrete wall to be constructed. It is $2 \mathrm{m}$ wide at the top, $3.5 \mathrm{m}$ wide at the bottom and its height is $6 \mathrm{m}$, and its length is $400 \mathrm{m}$. Calculate (i) the cross-sectional area, and (ii) volume of concrete in the wall.

The figure given below show the cross-section of a swimming pool $10 \mathrm{m}$ broad, $2 \mathrm{m}$ deep at one end and $3 \mathrm{m}$ deep at the other end. Calculate the volume of water it will hold when full, given that its length is $40 \mathrm{m}$.

A swimming pool is $50$ metres long and $15$ metres wide. Its shallow and deep ends are $1\frac{1}{2}$ metres and $4\frac{1}{2}$ metres deep respectively. If the bottom of the pool slopes uniformly, find the amount of water required to fill the pool.