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

Answer 1

Given diameter of golf ball = 4.1 cm  

=> radius of golf ball 

= diameter/2 = 4.1/2cm 

Now surface area of golf ball without dimples 

 $4 \pi r^{2} = 4 * \pi * (4.1/2)^{2} = 16.81 \pi c m^{2}$

 

It is given that the shape of dimples is hemispherical and radius of each dimple= 2mm = 0.2 cm 

Area of each dimple  =  

$= 2 \pi r^{2} = 2 * \pi * (0.2)^{2} = 0.08 \pi c m^{2}$

 

So area of 150 dimples = 150 x area of each dimple = 150 x 0.8π = 12π cm square  

Area of flat surface removed to make 1 dimple 

 $= \pi r^{2} = \pi * (0.2 )^{2} = 0.04 \pi c m^{2}$

 

 

Area of flat surface removed to make 150 dimples  

 [tex]= 150 * 0.04 \pi = 6 \pi c m^{2} [/tex]

 

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  

= 16.81 π + 12π - 6π = 22.81π cm square  

 

= 22.81 x 3.14 = 71.62 cm square