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 `= 4 π r^2`
Or, `4 π r^2 = 154`
Or, `r^2 = 154/4 \π`
`= (154 xx 7)/(4 xx 22) = (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


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 `= 2 π r^2`
`= 2 xx (22/7) xx 5.25 xx 5.25`
`= 33 xx 5.25 = 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 `= 4 π r^2`

(ii) curved surface area of the cylinder,

Asnwer: CSA of cylinder `= 2 π rh`
`= 2 π r xx 2r = 4 π r^2`

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

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



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