# 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: CSA 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