Question

A cylinder of radius 4 cm and height 10 cm is melted and re casted into a sphere of radius 2 cm. How many such sphere are got ?

• A. 25
• B. 30
• C. 15
• D. 28

Answer 1

Answer:

C. 15

The total number of spheres obtained is 30.

Step-by-Step Solution

When a 3D object is melted and recast into another shape, the total volume remains the same.

$\text{Number of Spheres} = \frac{\text{Volume of the Cylinder}}{\text{Volume of one Sphere}}$

1. Calculate the Volume of the Cylinder

• Formula: $V_{\text{cylinder}} = \pi r^2 h$

• Given: Radius ($r$) = $4\text{ cm}$, Height ($h$) = $10\text{ cm}$

• $V_{\text{cylinder}} = \pi \times 4^2 \times 10 = \pi \times 16 \times 10 = \mathbf{160\pi \text{ cm}^3}$

2. Calculate the Volume of a Sphere

• Formula: $V_{\text{sphere}} = \frac{4}{3}\pi R^3$

• Given: Radius ($R$) = $2\text{ cm}$

• $V_{\text{sphere}} = \frac{4}{3}\pi \times 2^3 = \frac{4}{3}\pi \times 8 = \mathbf{\frac{32}{3}\pi \text{ cm}^3}$

3. Find the Number of Spheres

• Divide the cylinder's volume by the sphere's volume ($\pi$ cancels out on both sides):
  $\text{Number of Spheres} = \frac{160\pi}{\frac{32}{3}\pi}$

• $\text{Number of Spheres} = 160 \times \frac{3}{32}$

• $\text{Number of Spheres} = 5 \times3 = \mathbf{15}$