A GOLF BALL HAS DIAMETER EQUAL TO 4.1CM. ITS SURFACE HAS 150 DIMPLES EACH OF RADIUS 2MM (0.2 CM) .CALCULATE TOTAL SURFACE AREA WHICH IS EXPOSED TO SURROUNDINGS ASSUMING THAT THE DIMPLES ARE HEMISPHERCAL.

• the total surface area of the golf ball without considering the dimples is 4*3.14*sqrt(4.1/2).
  Due to 150 pits on the surface a there will be a reduction in surface area of ball which will be equal to opening area of the dimples which is 150*3.04*sqrt(0.2). again due to formation of the pits there will be an increase in surface area due to hemispherical concave surface of the pits which will be 150*2*3.14*sqrt(0.2) .So, the total surface area will be 4*3.4*sqrt(4.1)-150*3.14*sqrt(.2)+150*2*3.14*sqrt(.2)=71.62cm2
• 8 years agoHelpfull: Yes(5) No(0)
• Given that diameter of golf ball = 4.1 cm
  
  Radius of golf ball = d / 2 = 4.1 / 2 = 2.05 cm
  
  Surface area of golf ball without dimples = 4πr2 = 4π(2.05)2 = 16.81π cm2
  
  Given that the shape of dimples is hemispherical and radius of each dimple = 2 mm = 0.2 cm
  
  ∴ area of each dimple =2πr2 = 2π(0.2)2 = 0.08π cm2
  
  So, area of 150 dimples = 150 × area of each dimple = 150 × 0.08π = 12πcm2
  
  Area of flat surface removed to make 1 dimple = πr2 = π(0.2)2 = 0.04π cm2
  
  ∴ area of flat surface removed to make 150 dimples = 150 x 0.04π = 6π cm2 .
  
  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
  
  Total surface area = 16.81π + 12π - 6π = 22.81π cm2
  
  Total surface area = 2.81x3.14
  
  ∴Total surface area = 71.62 cm2.
• 6 years agoHelpfull: Yes(5) No(0)
• http://www.meritnation.com/ask-answer/question/a-golf-ball-has-diameter-equal-to-4-1cm-its-surface-has-15/math/3281073
  71.62cm2
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