R. D. Sharma Solutions for Chapter: Mensuration-III (Surface Area and Volume of a Right Circular Cylinder), Exercise 2: EXERCISE

Find the volume of a cylinder, the diameter of whose base is $7 \mathrm{cm}$ and height being $60 \mathrm{cm}$. Also, find the capacity of the cylinder in litres.

The difference between inside and outside surfaces of a cylindrical tube $14 \mathrm{cm}$ long is $88 \mathrm{sq}. \mathrm{cm}$. If the volume of the tube is $176$ ${\mathrm{cm}}^3$, find the inner and outer radii of the tube. (Take $\mathrm{\pi }=\frac{22}{7}$)

Find the cost of sinking a tube well $280 \mathrm{m}$ deep, having diameter $3 \mathrm{m}$ at the rate of $₹3.60$ per cubic metre. Find also the cost of cementing its inner curved surface at $₹2.50$ per square metre.

$2.2$ cubic dm of brass is to be drawn into a cylindrical wire $0.25 \mathrm{cm}$ in diameter. Find the length of the wire. (Take $\mathrm{\pi }=\frac{22}{7}$)

A well with $10 \mathrm{m}$ inside diameter is dug $8.4 \mathrm{m}$ deep. Earth taken out of it is spread all around it to a width of $7.5 \mathrm{m}$ to form an embankment. Find the height of the embankment. (Take $\mathrm{\pi }=\frac{22}{7}$)

A hollow garden roller, $63 \mathrm{cm}$ wide with a girth of $440 \mathrm{cm}$, is made of $4 \mathrm{cm}$ thick iron. If the volume of the iron is $\mathrm{k} {\mathrm{cm}}^3$, then find $\mathrm{k}$ considering $\mathrm{\pi }=\frac{22}{7}$.

What length of a solid cylinder $2 \mathrm{cm}$ in diameter must be taken to recast into hallow cylinder of length $16 \mathrm{cm}$, external diameter $20 \mathrm{cm}$ and thickness $2.5 \mathrm{mm}$?

In the middle of a rectangular field measuring $30 \mathrm{m} \times 20 \mathrm{m}$ a well of $7 \mathrm{m}$ diameter and $10 \mathrm{m}$ depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.