If the total surface area of a solid hemisphere is 462 cm2, find its v

1.	If the total surface area of a solid hemisphere is 462 cm2, find its volume.(Take π = \(\frac{22}7\))
Answer» Total surface area of solid hemisphere = 3πr² ⇒ 3πr² = 462 ⇒ 3 × (\(\frac{22}7\)) × r² = 462 ⇒ r² = \(\frac{{462}\times{7}}{{22}\times{3}}\) ⇒ r² =49 ⇒ r = 7 cm Volume of solid hemisphere = \(\frac{2}3πr^3\) = \(\frac{2}3π7^3\) cm³ = \(\frac{2}{3}\times\frac{22}7\times7\times7\times7\) = 718.67 cm³

If the total surface area of a solid hemisphere is 462 cm2, find its volume.(Take π = \(\frac{22}7\))

Answer»

Total surface area of solid hemisphere = 3πr²

⇒ 3πr² = 462

⇒ 3 × (\(\frac{22}7\)) × r² = 462

⇒ r² = \(\frac{{462}\times{7}}{{22}\times{3}}\)

⇒ r² =49

⇒ r = 7 cm

Volume of solid hemisphere = \(\frac{2}3πr^3\)

= \(\frac{2}3π7^3\) cm³

= \(\frac{2}{3}\times\frac{22}7\times7\times7\times7\)

= 718.67 cm³