A golf ball has a diameter of 4.1cm and the surface has 150 dimples of radius 2mm Calculate the total surface area?

Answer 1

You didn't finish the question but I assume that you mean the surface area minus the area of the dimples.

The surface area of a sphere is 4π*r^2 and since the diameter is 4.1 cm, the radius is half of that or 2.05 cm.

Hence the surface area of a sphere of radius 2.05 = 4*π*(2.05)^2 =52.8101725 cm^2

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Now for the dimples. They are circles taken out of the surface of the sphere and hence each has an area of π*r^2 and there are 150 of these.

One cm is 10 mm (cm is hundredth, mm is thousandth)

So the radius of the dimples is 0.2cm

150 * π * (0.2)^2 = 150 * π * (0.04) = 6πcm^2 = 18.8495556 cm^2

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Now we subtract the area of the dimples from the area of the sphere:

52.8101725 cm^2

18.8495556 cm^2

------------------------------- Subtract

33.9606165 cm^2

ANSWER: 33.9606165 cm^2 is the surface area of the Golf ball minus the area of the dimples.