The volume of a sphere is 38,808 cm3. Then find the lateral surface ar

1.	The volume of a sphere is 38,808 cm3. Then find the lateral surface area of a hemisphere if the radius of a sphere is twice of a hemisphere.1. 693 cm22. 1296 cm23. 1456 cm24. 496 cm2
Answer» Correct Answer - Option 1 : 693 cm² Given: Volume of a sphere is 38,808 cm3 Radius of a sphere is twice of the hemisphere. Formula Used: Volume of a sphere = 4/3πr³ Lateral surface area of a hemisphere = 2πr² Calculation: Volume of a sphere = 4/3πr3 ⇒ 4/3π r3 = 38,808 ⇒ r3 = (38,808 × 3)/ 4π ⇒ r3 = 9261 ⇒ r = 21 As radius of a sphere is twice of a hemisphere. ⇒ radius_(circle) = 2 radius_(hemisphere) ⇒ 21 = 2 radius(hemisphere) ⇒ radius_(hemisphere) = 21/2 Now, Lateral surface area of a hemisphere = 2πr2 ⇒ Lateral surface area of a hemisphere = 2π × (21/2)² ⇒ Lateral surface area of a hemisphere = 693 ∴ The lateral surface area of a hemisphere is 693 cm².

The volume of a sphere is 38,808 cm3. Then find the lateral surface area of a hemisphere if the radius of a sphere is twice of a hemisphere.1. 693 cm22. 1296 cm23. 1456 cm24. 496 cm2

Answer» Correct Answer - Option 1 : 693 cm²

Given:

Volume of a sphere is 38,808 cm3

Radius of a sphere is twice of the hemisphere.

Formula Used:

Volume of a sphere = 4/3πr³

Lateral surface area of a hemisphere = 2πr²

Calculation:

Volume of a sphere = 4/3πr3

⇒ 4/3π r3 = 38,808

⇒ r3 = (38,808 × 3)/ 4π

⇒ r3 = 9261

⇒ r = 21

As radius of a sphere is twice of a hemisphere.

⇒ radius_(circle) = 2 radius_(hemisphere)

⇒ 21 = 2 radius(hemisphere)

⇒ radius_(hemisphere) = 21/2

Now, Lateral surface area of a hemisphere = 2πr2

⇒ Lateral surface area of a hemisphere = 2π × (21/2)²

⇒ Lateral surface area of a hemisphere = 693

∴ The lateral surface area of a hemisphere is 693 cm².

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