a golf ball has diameter equal to 4 1cm Its surface has 150 dimples each of radius 2mm - Maths - Surface Areas and Volumes

Question

a golf ball has diameter equal to 4 1cm Its surface has
150 dimples each of radius 2mm Calculate total surface area exposed
to the surrondings assuming that the dimples are
hemispherical
I WANT THE ANSWER WITH FUUL EXPLANATION AT EACH STEP
THE LINK WSA NOT ABLE TO SATISFY ME

Ankush Jain · Accepted Answer

Given, diameter of golf ball = 4 1 cm â‡’ radius of golf ball $= \frac{d i a m e t e r}{2} = \frac{4 1}{2} c m$ Now, surface area of golf ball without dimples $= 4 π r^{2} = 4 \times π \times (\frac{4 1}{2})^{2} = 16 81 π c m^{2}$ It is given that the shape of dimples is hemispherical and radius of each dimple = 2 mm = 0 2 cm âˆ´ area of each dimple = $= 2 π r^{2} = 2 \times π \times (0 2)^{2} = 0 08 π c m^{2}$ So, area of 150 dimples = 150 Ã— area of each dimple = 150 Ã— 0 08Ï€ = 12Ï€ cm2 Area of flat surface removed to make 1 dimple $= π r^{2} = π \times (0 2)^{2} = 0 04 π c m^{2}$ âˆ´ area of flat surface removed to make 150 dimples $= 150 \times 0 04 π = 6 π c m^{2}$ Now, total surface area of golf ball exposed to surroundings = surface area of golf ball without dimples + area of 150 dimples - area of flat surface removed to make 150 dimples = 16 81Ï€ + 12Ï€ - 6Ï€ = 22 81Ï€ cm2 $= 22 81 \times 3 14 = 71 62 c m^{2}$

a golf ball has diameter equal to 4.1cm. Its surface has 150 dimples each of radius 2mm. Calculate total surface area exposed to the surrondings assuming that the dimples are hemispherical. I WANT THE ANSWER WITH FUUL EXPLANATION AT EACH STEP. THE LINK WSA NOT ABLE TO SATISFY ME

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

I WANT THE ANSWER WITH FUUL EXPLANATION AT EACH STEP. THE LINK WSA NOT ABLE TO SATISFY ME