Surface Area

Exercise 13.2 Part 2

Question 6: Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height.

Answer: CSA = 4.4 sq m, r = 0.7 m, h = ?
CSA `= 2 π rh`
`Or, 2 xx (22/7) xx 0.7 xx h = 4.4`
`Or, h = (4.4)/(4.4) = 1 m`


Question 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 Rs 40 per m2.

Answer: d = 3.5 m. h = 10 m
CSA of cylinder `= π dh`
`= (22/7) xx 3.5 xx10 = 110 sq m`
Cost `= Ar\eaxxRa\te
`=110 xx 40 = Rs. 4400`

Question 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.

Answer: h = 28 m, d = 5 cm = 0.05 m
CSA of cylinder `= π dh`
`= (22/7) xx 0.05 xx 28 = 4.4 sq m`


Question 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.

Answer: d = 4.2 m so, r = 2.1 m, h = 4.5 m
CSA of cylinder `= π dh`
`=(22)/(7) xx 4.2 xx 4.5=59.40 sq m`

Total surface area of cylinder `= 2 π r(r + h)`
`= 2 xx (22/7) xx 2.1 (2.1 + 4.5)`
`=2xx(22/7)xx2.1xx6.6=87.12 sq m`

As 1/12 of steel is wasted so 11/12 of steel is used in making the cylinder
Hence, actual amount of used steel `= 87.12 xx (12/11) = 95.04 sq m`

Question 10: In the given figure, you see the 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.

question figure lampshade

Answer: d = 20 cm, h = 30 cm, margin = 2.5 cm
Effective `h = 30 + 2.5 + 2.5 = 35 cm`
CSA of cylinder `= 2π rh`
`= 2 xx (22/7) xx 20 xx 35 = 2200 sq cm`

Question 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?

Answer: r = 3 cm, h = 10.5 cm, no. of penholders = 35
CSA of cylinder `= 2 π rh`
`= 2 xx (22/7) xx 3 xx 10.5 = 198 sq cm`
Hence, CSA of 35 cylinders `= 198 xx 35 = 6930 sq cm`

Area of base `= π r^2= (22/7) xx 3^2=(22/7)xx9`
Hence, area of 35 base `= 35 xx (22/7) xx 9 = 990 sq cm`
Total area of required cardboard `= 6930 + 990 = 7920 sq cm`



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