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

CSA 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,

question figure of sphere inside cylinder

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



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