A golf ball has diameter equal to 4.2 cm. Its surface has 200 dimples each of radius 2 mm. Calculate the total surface area which is exposed to the surroundings assuming that the dimples are hemispherical.
Answers
Answer:
The Total surface area exposed is 80.58 cm².
Step-by-step explanation:
SOLUTION :
Given :
Diameter of golf ball = 4.2 cm
Radius of golf ball = d /2 = 4.2 / 2 = 2.1 cm
Surface area of golf ball without dimples = 4πr²
= 4π(2.1)² = 17.64 π cm²
Surface area of golf ball without dimples = 17.64 π cm²
Given: shape of dimples is hemispherical and radius of each dimple = 2 mm = 2/10 = 0.2 cm
[ 1 mm = 1/10 cm]
Area of each dimple (hemisphere) = 2πr²
= 2π(0.2)² = 0.08π cm²
Area of each dimple (hemisphere) = 0.08π cm²
Area of 200 dimples = 200 × Area of each dimple
= 200 × 0.08π = 16π cm²
Area of 200 dimples = 16π cm²
Area of flat surface removed to make 1 dimple = πr²
= π(0.2)² = 0.04π cm²
Area of flat surface removed to make 200 dimples = 200 x 0.04π = 8π cm² .
Area of flat surface removed to make 200 dimples = 8π cm² .
Total surface area of golf ball exposed to surroundings = surface area of golf ball without dimples + Area of 200 dimples - Area of flat surface removed to make 200 dimples
Total surface area exposed = 17.64 π + 16π - 8π
= 17.64 π + 8π
= π(17.64 + 8)
= 22/7 × 25.64 = 564.08/7
Total surface area exposed = 80.58 cm²
Hence, the Total surface area exposed is 80.58 cm².
HOPE THIS ANSWER WILL HELP YOU….
ANSWER :
Total surface area exposed = 80.58 cm²
Diameter of golf ball = 4.2 cm
=>Radius of golf ball = d /2 = 4.2 / 2 = 2.1 cm
S.A. of golf ball without dimples = 4πr²
= 4π(2.1)² = 17.64 π cm²
- Shape of dimples is hemispherical
Radius of each dimple = 2 mm = 2/10 cm = 0.2 cm
[ 1 mm = 1/10 cm]
Area of each dimple (hemisphere) = 2πr²
= 2π(0.2)² = 0.08π cm²
Area of each dimple = 0.08π cm²
Area of 200 dimples = 200 × Area of each dimple
= 200 × 0.08π = 16π cm²
Area of 200 dimples = 16π cm²
Area of surface removed to make 1 dimple = πr²
r=0.2(given)
= π(0.2)² = 0.04π cm²
Area of flat surface removed to make 200 dimples = 200 x 0.04π = 8π cm²
Total surface area of golf ball exposed to surroundings =
Surface area of golf ball without dimples + Area of 200 dimples - Area of flat surface removed to make 200 dimples
Total surface area exposed =>
= 17.64 π + 16π - 8π
= 17.64 π + 8π
= π(17.64 + 8)
= 22/7 × 25.64 = 564.08/7
= 80.58 cm²
Hence, the Total surface area exposed is 80.58 cm².
Hope this helps ...