Question

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

Answer 1

the answer Is 27.62cm^2

Answer 2

Answer:

$\huge\underline{\rm\red{Reticent_Bliss}}$

Step-by-step explanation:

$\underline\green{Total~Surface~area~without~dimples}$ = $4 \times \frac{22}{7} \times (2.05) ^{2} \\ \\ = > 52.83 \: {cm}^{2}$

$\underline\green{Total~area~with~dimples}$ = $\frac{22}{7} \times (0.2) ^{2} \times 150 \\ \\ = > 18.857 \: {cm}^{2}$

$\underline\green{Area~where~there~are~no~dimples}$ = $52.83 - 18.857 \\ \\ = > 33.973 \: {cm}^{2}$

$\underline\green{Area~of~the~dimples}$ = $\frac{1}{2} \times 4 \times \frac{22}{7} \times (0.2) ^{2} \times 150 \\ \\ = > 37.714 \: {cm}^{2}$

$\red{Surface~area~exposed~to~surroundings}$ ☺☺☺↓↓↓☺☺☺↓↓↓☺☺☺ $\blue{Area~with~no~dimples~+~Area~of~dimples}$

$= > 33.973 + 37.714 \\ \\ = = = > 71.687 \: {cm}^{2}$

$\huge\underline{\rm\red{Reticent_Bliss}}$