Question

A golf ball has diameter equal to 4.1 cm.its surface has 150 dimples each of radius 2mm calculate t s a which is exposed to the surroundings

Answer 1

Answer:

71.6cm²

Step-by-step explanation:

Given : diameter=4.1cm

radius = 2.05cm.

therefore , total surface area of a sphere = 4πr²

calculation= 4× 22/7 × (2.05)²

= 4×22/7×4.2025

= 22/7 × 16.81

= 22 × 2.4 (approx)

= 52.8 cm²

Now, no. of dimples = 150.

radius = 2mm or 0.2cm(it's the max cross sectional area)

now , taking the maximum cross section area/the cross section area of the middle slice of the sphere which has the max area = circle = πr²

=>22/7 × (0.2)² = 22/7 × 0.04

=> 0.88/7 = 0.125cm²

now all total area = 0.125 × 150cm²

= 18.9cm²(approx)

subtracting the 2D areas from the sphere =

(52.8-18.9)cm²= 33.9cm²

Now, as the dimples are deep / are 3D , we need the t s a of the hemisphere of the dimples.

[EXPLANATION :- We know that , when we dig a hemisphere on a surface (golf bol has hemispheres dig in it), the topmost part from where the digging was start has the area of the max cross section of the same hemisphere . Now by digging , we made an extra surface area , as the area has increased which now contains the t s a of the hemisphere . Please read it twice and include logic and experimentation to understand the explanation if not understood by any of u ]

Therefore, we know , lateral surface area of a hemisphere (area excluding it's base as it has been already removed) is = 2πr²

=> 2 × 22/7 × (0.2)² = 1.76/7

=> 0.251×150 = 37.7 (approx)

Therefore, adding this area to the obtained area => (33.9+37.7) = 71.6cm²

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for any mistakes , pls pardon.

THANKS !!