Surface Area

Exercise 13.4

Part 2

Question 6: Find the radius of a sphere whose surface area is 154 cm²

Answer: Surface area = 154 sq cm

Curved Surface Area of sphere `=4πr^2`

Or, `4πr^2=154`

Or, `r^2=(154)/(4π)`

`=(154xx7)/(4xx22)=(7/2)xx(7/2)`

Or, `r=7/2=3.5` cm

Question 7: The diameter of the moon is approximately one fourth of the diameter of the earth. Find the ratio of their surface areas.

Answer: Surface areas of spheres are in duplicate ratio of their radii.

Here; `R : r = 4 : 1`

Hence, `A : a = 4^2 : 1^2= 16 : 1`

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

This question can solved as follows, by conventional method:

Let us assume, radius of earth = r

Then radius of moon `=r/4`

Surface area of earth `=4πr^2`

Surface area of moon `=4π(r/4)^2=1/4πr^2`

Ratio of areas `=(4πr^2)/(1/4πr^2)` =16 : 1

Question 8: A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.

Answer: Answer: Inner radius = 5 cm and thickness = 0.25 cm

Hence, outer radius = 5 + 0.25 = 5.25 cm

Outer CSA of hemisphere `=2πr^2`

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

`=33xx5.25=173.25` sq cm

Question 9: A right circular cylinder just encloses a sphere of radius r. Find
(i) surface area of the sphere,

Answer: Surface area of sphere `=4πr^2`

(ii) curved surface area of the cylinder,

Asnwer: CSA of cylinder `=2π\rh`

`=2πr\xx2r=4πr^2`

(iii) ratio of the areas obtained in (i) and (ii)

Answer: Ratio `=(4πr^2)/(4πr^2)` = 1 : 1