FORMULA:
Curved Surface Area of a Cylinder = $2 πrh$
Total Surface Area of a Cylinder = $2πr(r + h)$
where $r$ = radius of the base of cylinder
$h$ = height of cylinder
Assume π = $22/7$ unless stated otherwise
1. The curved surface area of a right circular cylinder of height 14 cm is 88 $cm^2$. Find the diameter of the base of the cylinder.
2. It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square metres of the sheet are required for the same?
3. A metal pipe is 77 $cm$ long. The inner diameter of a cross section is 4 $cm$, the outer diameter being 4.4 $cm$ (see Fig. 13.11). Find its
(i) inner curved surface area,
(ii) outer curved surface area,
(iii) total surface area.
4. The diameter of a roller is 84 $cm$ and its length is 120 $cm$. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in $m^2$.
5. A cylindrical pillar is 50 $cm$ in diameter and 3.5 $m$ in height. Find the cost of painting the curved surface of the pillar at the rate of ₹ 12.50 per $m^2$.
6. Curved surface area of a right circular cylinder is 4.4 $m^2$. If the radius of the base of the cylinder is 0.7 $m$, find its height.
7. The inner diameter of a circular well is 3.5 $m$. It is 10 $m$ deep. Find
(i) its inner curved surface area,
(ii) the cost of plastering this curved surface at the rate of ₹ 40 per $m^2$.
8. In a hot water heating system, there is a cylindrical pipe of length 28 $m$ and diameter 5 $cm$. Find the total radiating surface in the system.
9. Find
(i) the lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 $m$ in diameter and 4.5 $m$ high.
(ii) how much steel was actually used, if $1/12$ of the steel actually used was wasted in making the tank.
10. You have a frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 $cm$ and height of 30 $cm$. A margin of 2.5 $cm$ is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
11. The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder was to be of radius 3 $cm$ and height 10.5 $cm$. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?