# Surface Area

## Exercise 13.4

### Part 1

Question 1: Find the surface area of a sphere of radius:
(i) 10.5 cm

Answer: Surface area of sphere =4πr^2

=4xx(22)/7xx10.5xx10.5

=132xx10.5 = 1386 sq cm

(ii) 5.6 cm

Answer: Surface area of sphere =4πr^2

=4xx(22)/7xx5.6xx5.6=394.24 sq cm

(iii) 14 cm

Answer: Surface area of sphere =4πr^2

=4xx(22)/7xx14xx14=2464 sq cm

Question 2: Find the surface area of a sphere of diameter:
(i) 14 cm

Answer: Surface area of sphere =4πr^2

=4xx(22)/7xx7xx7=616 sq cm

(ii) 21 cm

Answer: Surface area of sphere =4πr^2

=4xx(22)/7xx10.5xx10.5=1386 sq cm

(iii) 3.5 m

Answer: Surface area of sphere =4πr^2

=4xx(22)/7xx1.75xx1.75=38.5 sq cm

Question 3: Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)

Answer: Total surface area of hemisphere =3πr^2

=3xx3.14xx10xx10=942 sq cm

Question 4: The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.

Answer: r_1=7 cm, r_2=14 cm

Surface area of smaller balloon =4πr^2

=4π\xx7^2=4π\xx49

Surface area of bigger balloon =4πr^2

=4π\xx14^2=4π\xx196

Ratio of areas =(4π\xx49)/(4π\xx196) = 1 : 4

Area of two similar shapes is in duplicate ratio of the ratio of their dimensions. This means when radius becomes double then surface area becomes four times, i.e. 22

Question 5: A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of Rs 16 per 100 cm2.

Curved surface area of hemisphere =2πr^2

=2xx(22)/7xx5.25xx5.25

=33xx5.25=173.25 sq cm

Cost = Area × Rate

=173.25xx(16)/(100) = Rs. 27.72