# Find the Diameter of Each Sphere ?

Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is;

- 2cm
- 3 cm
- 4 cm
- 6 cm

**Answer: (1) 2 cm**

**Explanation:-
**

**Formula-**

Volume of the cylinder V = Pai x r

Where, r = radius, h = height

Volume of the cylinder V = Pai x r

^{2}x hWhere, r = radius, h = height

Then, V = pai x 1 x 16

V = 16 pai

divide by 12,

Then, the volume of a small cylinder = 16 pai/12

= 4 pai /3

**Formula-
Volume of sphere = 4 pai x (d/2) ^{3}
radius = diameter/2**

Then, volume of sphere = 4 pai (d/2)^{3}/3

4 pai/3 = 4 pai (d/2)^{3}/3

1 = (d/2)^{3}

Cube root on both side,

1 = d/2

by cross multiplication,

d = 2 cm

Then, the diameter of the sphere is 2 cm.

Hence, the answer is ** (1) 2 cm.**