A golf ball has diameter equal to 4.1 cm. Its surface has 150 dimples each of radius 2 mm
Calculate total surface area which is exposed to the surroundings. (Assume that the dimples
22
are all hemispherical) =
7
22
Answers
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We have
Diametre of golf ball= 4.1cm
radius of each dimplets= 2mm
surface area of the ball =4πr
2
=4π×(
2
4.1
)
2
cm
2
=16.81cm
2
In case of each dimplets, surface area equal to πr
2
(r is the radius of each dimple) is removed from the surface of the ball where as the surface area of hemisphere i.e 2πr
2
is exposed to the surroundings
Total surface area exposed to the surroundings = surface area of the ball
−150πr
2
+150×2πr
2
=16.81π+150πr
2
=
⎩
⎪
⎨
⎪
⎧
16.81π+150π×(
10
2
)
2
⎭
⎪
⎬
⎪
⎫
cm
2
=22.81×
7
22
cm
2
=71.68cm
2
Thnks..
Answer:
71.7 cm²
Step-by-step explanation:
Given,
Diameter = 4.1 cm
Radius = Diameter/2 = 2.05 cm.
Surface area of ball = 4πr²
=> 4π * (2.05)²
⇒ 16.81π cm²
Also Given that,
Shape of dimples is hemispherical and radius= 2mm = 0.2 cm.
Area of 150 dimples = 150 * 2πr² = 12πcm².
Area of flat surface removed to make 1 dimple = 0.04π cm²
Area of flat surface removed to make 150 dimples :
= 150 * 0.04
= 6π cm²
TSA of golf ball exposed to surroundings :
= 16.81π + 12π - 6π
= 22.81π
= 71.7 cm²
Hope it helps!