Question

A metallic sphere of radius 8.4 CM is melted and recost into the shape of a cylinder of radius 4 CM. show that the height of the cylinder is 49.4 cm​

Answer 1

Answer:

Step-by-step explanation: Even when recast, the volume of the material will remain the same.

So, 4/3 π r₁³ = π r₂² h

On cancelling π, 4/3 (8.4)³ = (4)² h

4/3 × 592.704 = 790.272 = 16h

h = 790.272 / 16 = 49.392  ≈ 49.4 cm

Answer 2

Question :--- A metallic sphere of radius 8.4 CM is melted and recost into the shape of a cylinder of radius 4 CM. show that the height of the cylinder is 49.4 cm ?

Formula and concept used :---

→ when anything is melted and recast into another shape, their volume will be same in both case..

→ volume of sphere = 4/3 * π * r³

→ Volume of cylinder = π * r² * h .

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Solution :---

putting values in both formula and comparing their volume now we get,

→ 4/3 * π * r³ = π * r² * h

π will be cancel from both sides ,

→ 4/3 * (8.4)³ = (4)² * h

→ (8.4)³ = 4 * 3 * h

→ (8.4) ³ = 12 * h

→ h = (8.4*8.4*8.4)/12

→ h = 49.39 .

Hence, Height of cylinder will be 49.4 (Approx).