A solid top is in the shape of a cone surmounted by a hemisphere. If the total volume of the solid is 2816 cm³ and the radius of the hemispherical part is 8 cm, find the height of the top.
(Take π = 22/7)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 34 cm.
Volume of hemisphere = (2/3) × π × r³ = (2/3) × (22/7) × 8³
⇒ (2/3) × (22/7) × 512 = (2 × 22 × 512) / (3 × 7) = 22528 / 21 ≈ 1072 cm³
Total volume = Volume of hemisphere + Volume of cone
Volume of cone = 2816 − 1072 = 1744 cm³
(1/3) × (22/7) × 8² × h = 1744
→ (1/3) × (22/7) × 64 × h = 1744
→ (1408/21) × h = 1744
→ h = 1744 × (21 / 1408) = 26 cm
The height of the top = h + r = 26 + 8 = 34 cm