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A golf ball has diameter equal to $4.1 cm .$ Its surface has 150 dimples each of radius $2 mm$ . What is the total surface area which is exposed to the surroundings, assuming that the dimples are hemispherical?

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61.68 cm 2

71 cm 2

61 cm 2

124.52 cm 2

answer is D.

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Detailed Solution

Given that the diameters of the golf ball equal to 4.1cm, number of dimples its surface has is150 and the radius of the dimples is 2mm.
We have the following formulae,
Area of the circle =

π r 2

CSA of the sphere =

4 π R 3

CSA of hemisphere =

2 π r 2

Assuming that the dimples are hemispherical,

R = 4.1 2 cm

r = 2 m m (1cm=10mm) = 210 c m = 0.2 c m

The total surface area which is exposed to the surroundings = CSA of golf ball

− 150

(Area of circle)

+ 150

(CSA of hemisphere)

= 4 π R 2 − 150 π r 2 + 150 2 π r 2

= 4 π R 2 + 150 π r 2

= 227 4 4.1 2 2 + 150 (0.2) 2

= 124.52 cm 2

Thus the total surface area is

124.52 cm 2

.
Therefore the correct option is 4.

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