A golf ball has a diameter equal to $4.2 c m$ . Its surface has $200$ dimples each of radius $2 m m$ . Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.

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Solution

The total surface area of golf ball exposed to surroundings will be equal to the surface area of a golf ball without dimples plus area of $200$ dimples and then we have to subtract the area of flat surface hidden by dimples
$\begin{matrix} A & = 4 π r^{2} + 200 \times 2 π r_{1}^{2} - 200 \times π r_{1}^{2} = 4 π [{(2.1)}^{2} + 100 \times {(0.2)}^{2} - 50 \times {(0.2)}^{2}] = 80.58 c m^{2} \end{matrix}$

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A golf ball has a diameter equal to 4.2cm. Its surface has 200 dimples each of radius 2mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.

The total surface area of golf ball exposed to surroundings will be equal to the surface area of a golf ball without dimples plus area of 200 dimples and then we have to subtract the area of flat surface hidden by dimplesA=4πr2+200×2πr21−200×πr21=4π[(2.1)2+100×(0.2)2−50×(0.2)2]=80.58cm2

A golf ball has a diameter equal to $4.2 c m$ . Its surface has $200$ dimples each of radius $2 m m$ . Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.