A cylinder of height 4 cm and base radius 3 cm is melted to form a sphere. The radius of sphere is:
1. 3 cm
2. 3.5 cm
3. 4 cm
4. 2.5 cm
1. 3 cm
2. 3.5 cm
3. 4 cm
4. 2.5 cm
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Correct Answer – Option 1 : 3 cm
Given:
Radius of cylinder = 3 cm
Height of cylinder = 4 cm
Formula Used:
Volume of cylinder = π (Radius)2 Height
Volume of sphere = (4/3)π (Radius)3
Concept Used:
One figure is melted and another figure is formed from that in this case volumes of both the figures will be equal.
Calculation:
Volume of cylinder = π (3 cm)2 (4 cm)
⇒ π × 9 × 4 cm3
⇒ 36π cm3
Volume of sphere = (4/3)π (Radius)3
⇒ (4/3)π (Radius)3 = 36π cm3
⇒ (Radius)3 = 27 cm3
⇒ Radius = 3 cm
∴ Radius of the sphere is 3 cm.