A cylinder of height 4 cm and base radius 3 cm is melted to form a sph

1.	A cylinder of height 4 cm and base radius 3 cm is melted to form a sphere. The radius of sphere is:1. 3 cm2. 3.5 cm3. 4 cm4. 2.5 cm
Answer» 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.

A cylinder of height 4 cm and base radius 3 cm is melted to form a sphere. The radius of sphere is:1. 3 cm2. 3.5 cm3. 4 cm4. 2.5 cm

Answer» 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.

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