a golf ball has diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate total surface area exposed to the surrondings assuming that the dimples are hemispherical.
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Total surface area without dimples = 4 x 22/7 x 2.05² = 52.83 cm²
Total area where the dimples are = 22/7 x 0.2² x 150 = 18.857 cm²
Area where there are no dimples = 52.83 - 18.857 = 33.973 cm²
Area of the dimples = 1/2 x 4 x 22/7 x 0.2² x 150 = 37.714 cm²
Surface area exposed to surroundings = Area with no dimples + area of dimples
= 33.973 + 37.714 = 71.687 cm²
Total area where the dimples are = 22/7 x 0.2² x 150 = 18.857 cm²
Area where there are no dimples = 52.83 - 18.857 = 33.973 cm²
Area of the dimples = 1/2 x 4 x 22/7 x 0.2² x 150 = 37.714 cm²
Surface area exposed to surroundings = Area with no dimples + area of dimples
= 33.973 + 37.714 = 71.687 cm²
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