The total surface area of a solid hemisphere is 4158 cm². Find its volume. [Take π = 22/7]

Explanation

Step 1: Write total surface area formula
Total SA = Curved surface + Base circle
= 2πr² + πr²
= 3πr²

Step 2: Set up equation
3πr² = 4158
3 × (22/7) × r² = 4158
(66/7)r² = 4158

Step 3: Solve for r²
r² = 4158 × 7/66
r² = 29,106/66
r² = 441

Step 4: Find radius
r = √441
r = 21 cm

Step 5: Calculate volume
Volume of hemisphere = (2/3)πr³
= (2/3) × (22/7) × (21)³
= (2/3) × (22/7) × 9261
= (2 × 22 × 9261)/(3 × 7)
= 407,484/21
= 19,404 cm³