QQuestion
A hollow sphere of external diameter 10 cm and internal diameter 6 cm is melted and made into a solid right circular cone of height 8 cm. Find the radius of the cone so formed.
(Use π = \frac{22}{7})
ICSEClass 10MathematicsMensuration04 Mark2025 Moderate
✓Answer
External radius of the hollow sphere, R = 5 cm
Internal radius of the hollow sphere, r = 3 cm
Height of the cone, h = 8 cm
Volume of metal in the hollow sphere = \frac{4}{3}π(R³ − r³)
= \frac{4}{3}π(5³ − 3³)
= \frac{4}{3}π(125 − 27)
= \frac{392}{3}π cm³
Let the radius of the cone be m cm.
Volume of the cone = \frac{1}{3}πm²h
= \frac{1}{3}πm² × 8
= \frac{8}{3}πm²
Since the sphere is melted to form the cone, their volumes are equal.
\frac{392}{3}π = \frac{8}{3}πm²
⇒ 392 = 8m²
⇒ m² = 49
⇒ m = 7 cm
Therefore, the radius of the cone is 7 cm.
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