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A golf ball is spherical with about $300 - 500$ dimples that help increase its velocity while in play. Golf balls are traditionally white but available in colours also. In the given figure, a golf ball has diameter $4.2$ cm and the surface has $315$ dimples (hemi-spherical) of radius $2$ mm.
Based on the above, answer the following questions :
(i) Find the surface area of one such dimple.
(ii) Find the volume of the material dug out to make one dimple.
(iii) (a) Find the total surface area exposed to the surroundings.
OR
(iii) (b) Find the volume of the golf ball.
Based on the above, answer the following questions :
(i) Find the surface area of one such dimple.
(ii) Find the volume of the material dug out to make one dimple.
(iii) (a) Find the total surface area exposed to the surroundings.
OR
(iii) (b) Find the volume of the golf ball.
Show SolutionHide Solution↓
(i) $SA = 2\pi r^2 = 2 \times \frac{22}{7} \times 4 = \frac{176}{7} \text{ mm}^2$ or $25.1 \text{ mm}^2$
(ii) Volume of material dug out to make one dimple $= \frac{2}{3} \times \frac{22}{7} \times 8 = \frac{352}{21} \text{ mm}^3$ or $16.76 \text{ mm}^3$
(iii)(a) radius of ball $= 21$ mm
Total surface area exposed to surroundings
$= 4\pi(21)^2 - 315 \times \pi(2)^2 + 315 \times 2\pi(2)^2$
$= 4 \times \frac{22}{7} \times 21 \times 21 + \frac{22}{7} \times 315 \times 4$
$= 9504 \text{ mm}^2$
OR
(iii) (b) Volume of the golf ball $= \frac{4}{3}\pi(21)^3 - 315 \times \frac{2}{3}\pi(2)^3$
$= 33528 \text{ mm}^3$
(ii) Volume of material dug out to make one dimple $= \frac{2}{3} \times \frac{22}{7} \times 8 = \frac{352}{21} \text{ mm}^3$ or $16.76 \text{ mm}^3$
(iii)(a) radius of ball $= 21$ mm
Total surface area exposed to surroundings
$= 4\pi(21)^2 - 315 \times \pi(2)^2 + 315 \times 2\pi(2)^2$
$= 4 \times \frac{22}{7} \times 21 \times 21 + \frac{22}{7} \times 315 \times 4$
$= 9504 \text{ mm}^2$
OR
(iii) (b) Volume of the golf ball $= \frac{4}{3}\pi(21)^3 - 315 \times \frac{2}{3}\pi(2)^3$
$= 33528 \text{ mm}^3$