Question

How many spherical balls can be made out of a solid cube of iron whose edge measures 44 cm and each ball being 4 cm in diameter? (Take \( \pi = \frac{22}{7} \))

• A. 2541
• B. 5241
• C. 2514
• D. 3514

Hint:

To calculate the number of spherical balls that can be made from a cube, divide the volume of the cube by the volume of one ball. Ensure to use the correct formula for the volume of a sphere and take appropriate values of \( \pi \) and the radius.

Answer 1

The Correct Option is A

Step 1: Calculate the Volume of the Cube The volume \( V \) of a cube is given by: \[ V = \text{side}^3 \] Here, the side of the cube is 44 cm, so the volume of the cube is: \[ V = 44^3 = 44 \times 44 \times 44 = 85184 \, \text{cm}^3 \]

Step 2: Calculate the Volume of One Sphere The formula for the volume \( V \) of a sphere is: \[ V = \frac{4}{3} \pi r^3 \] Given the diameter of each ball is 4 cm, the radius \( r \) is: \[ r = \frac{4}{2} = 2 \, \text{cm} \] Substitute the values into the formula: \[ V = \frac{4}{3} \times \frac{22}{7} \times 2^3 = \frac{4}{3} \times \frac{22}{7} \times 8 = \frac{704}{21} \approx 33.52 \, \text{cm}^3 \]

Step 3: Find the Number of Spherical Balls To find the number of spherical balls, divide the volume of the cube by the volume of one sphere: \[ \text{Number of balls} = \frac{85184}{33.52} \approx 2541 \]

Step 4: Conclusion Therefore, the number of spherical balls that can be made is \( 2541 \).