A cylindrical rod of radius 30 cm and length 40 cm is melted and made into spherical balls of radius 1 cm. the number of spherical balls is .
.
30 सेमी त्रिज्या की और 40 सेमी लंबी बेलनाकार छड़ को गलाया जाता है और 1 सेमी त्रिज्या की गोलियां बनाई जाती है। गोलियों की संख्या कितनी होगी?

Options

A. 40000
B. 90000
C. 27000
D. 36000

Explanation

To find the number of spherical balls that can be made from a cylindrical rod, we need to calculate the volume of the cylinder and the volume of one spherical ball, and then divide the total volume of the cylinder by the volume of one ball.

### Step-by-Step Solution:

1. **Calculate the volume of the cylindrical rod:**
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height (length) of the cylinder.

Given:
- Radius \( r = 30 \) cm
- Height \( h = 40 \) cm

Substitute the values into the formula:
\[ V = \pi (30)^2 (40) \]
\[ V = \pi (900) (40) \]
\[ V = 36000\pi \text{ cubic cm} \]

2. **Calculate the volume of one spherical ball:**
The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.

Given:
- Radius \( r = 1 \) cm

Substitute the value into the formula:
\[ V = \frac{4}{3} \pi (1)^3 \]
\[ V = \frac{4}{3} \pi (1) \]
\[ V = \frac{4}{3}\pi \text{ cubic cm} \]

3. **Calculate the number of spherical balls:**
To find the number of balls \( x \), we divide the volume of the cylinder by the volume of one spherical ball:
\[ x = \frac{\text{Volume of cylinder}}{\text{Volume of one ball}} = \frac{36000\pi}{\frac{4}{3}\pi} \]
The \( \pi \) cancels out:
\[ x = \frac{36000}{\frac{4}{3}} = 36000 \times \frac{3}{4} = 27000 \]

Thus, the number of spherical balls that can be made is **27000**.