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.