If the total surface area of a solid hemisphere is 462 cm², find its volume. [Take π = 22/7]

We need to find the volume if the total surface area of a solid hemisphere is

462 𝑐𝑚² .

It is known that the TSA of hemisphere is given by 𝑇𝑆𝐴 = 3π𝑟², where 𝑟 is the radius of the hemisphere.

On substituting the given value of TSA, we get

⇒ 𝑇𝑆𝐴 = 3π𝑟²

⇒ 462 = 3π𝑟²

⇒ 154 = π𝑟²

⇒ 49 = 𝑟²
⇒ 𝑟 = 7 𝑐𝑚
Now, the volume of the hemisphere is given by 𝑉 = 2/3 π𝑟³.
On substituting the values, we get the volume as
𝑉 = 2/3 π𝑟³
⇒ 𝑉 = 2/3 x 22/7 x 7³
⇒ 𝑉 = 718. 67 𝑐𝑚³
Hence, the volume of the hemisphere 718.67 cm³