Surface Area

Exercise 13.2

Part 1

Question 1: The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.

Answer: Curved Surface Area of cylinder = 88 sq cm, h = 14 cm

CSA of cylinder `=2πr\h`

Or, `2πr\xx14=88`

Or, `2r=(88xx7)/(22xx14)=2`

Or, diameter = 2 cm

Question 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?

Answer: Diameter = 140 cm so, r = 70 cm, h = 100 cm

CSA of cylinder `=2π\rh`

`=2xx(22)/7xx70xx100=44000` sq cm

Area of top and bottom `=2πr^2`

`=2xx(22)/7xx70xx70=30800` sq cm

Total surface area of cylinder = 44000 + 30800 = 74800 sq cm = 7.48 sq m

Question 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. Find its

(i) inner curved surface area,

Answer: h = 77 cm, r₁ = 2 cm, r₂ = 2.2 cm

Inner curved surface area `=2πrh`

`=2xx(22)/7xx2xx77=968` sq cm

(ii) outer curved surface area,

Answer: Outer curved surface area `=2πrh`

`=2xx(22)/7xx2.2xx77=1064.8` sq cm

(iii) total surface area.

Answer: Area of top `=πr_2^2-πr_1^2`

`=π(r_2^2-r_1^2)=π(r_2+r_1)(r_2-r_1)`

`=π(2.2+2)(2.2–2)`

`=(22)/7xx4.2xx0.2=2.64` = area of bottom

Hence, total surface area = 968 + 1064.8 + 2.64 + 2.64 = 2038.04 sq cm

Question 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 m².

Answer: d = 84 cm, h = 120 cm

CSA `=π\dh`

`=(22)/7xx84xx120=31680` sq cm = 3.168 sq m

Hence, area of playground `=3.168xx500=1584` sq m

Question 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 Rs 12.50 per m².

Answer: d = 50 cm = 0.5 m, h = 3.5 m

CSA of cylinder `=π\dh`

`=(22)/7xx0.5xx3.5=5.5` sq m

Cost = Area × Rate `=5.5xx12.50` = Rs. 68.75