# Surface Area

## Exercise 13.3

### Part 1

Question 1: Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area.

Answer: d = 10.5 so, r = 5.25 cm, l = 10 cm

Curved surface area of cone =π\rl

=(22)/7xx5.25xx10=22xx7.5=165 sq cm

Question 2: Find the total surface area of a cone, if its slant height is 21 m and diameter of its base is 24 m.

Answer: d = 24 m so, r = 12 m, l = 21 m

CSA of cone =π\rl

=(22)/7xx12xx21

=66xx12=792 sq m

Area of base =πr^2

=(22)/7xx12xx12=452.16 sq m

Total surface area = 792 + 452.16 = 1244.16 sq m

Question 3: Curved surface area of a cone is 308 cm2 and its slant height is 14 cm. Find (i) radius of the base and (ii) total surface area of the cone.

Answer: CSA = 308 sq cm, l = 14 cm, r = ?

CSA =π\rl

Or, 308=(22)/7xx\r\xx14

Or, r=(308)/(44)=7 cm

Question 4: A conical tent is 10 m high and the radius of its base is 24 m. Find
(i) slant height of the tent.

Answer: Slant height can be calculated by using Pythagoras Theorem

l^2=h^2+r^2

=10^2+24^2=100+576=676

Or, l=sqrt(676)=26 cm

(ii) cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.

Answer: Answer: CSA of cone =π\rl

=(22)/7xx24xx26

Hence, Cost = Area × Rate

=(22)/7xx24xx26xx70 = Rs. 137280