Question

A clay cylinder of height 42 cm is converted into a cone of the same radius as that of the cylinder. If the volume of the cylinder is 52,800 cm3 , then the radius (in cm) of the cone is:(Use π =22/7)

• A. 20
• B. 24
• C. 18
• D. 22

Answer 1

Answer:

A. 20

The radius of the cone is 20 cm.

1. Understand the Relationship
The problem states that the cone has the same radius ($r$) as the cylinder. Therefore, we can find the radius directly by using the formula for the volume of a cylinder.

2. Use the Cylinder Volume Formula
The volume of a cylinder ($V$) is given by:
$V = \pi r^2 h$

Given:

• $V = 52,800 \text{ cm}^3$

• $h = 42 \text{ cm}$

• $\pi = \frac{22}{7}$

3. Substitute the Values and Solve for $r$
$52,800 = \frac{22}{7} \times r^2 \times 42$

Simplify the right side by dividing 42 by 7:
$52,800 = 22 \times r^2 \times 6$
$52,800 = 132 \times r^2$

Now, isolate $r^2$:
$r^2 = \frac{52,800}{132}$
$r^2 = 400$

Take the square root of both sides to find $r$:
$r = \sqrt{400} = 20 \text{ cm}$

Final Answer

The radius of the cone is 20 cm.