Samrudh has a solid metal ball with a diameter of 9 cm. He melts it and uses the material to make a solid cylinder. If the diameter of the cylinder is same as the ball, then what would be the height of the cylinder?

Correct option is A

Given:

Diameter of the solid metal ball (sphere): 9 cm

Diameter of the solid cylinder: 9 cm

Formula Used:

Volume of a sphere: V=$$\frac 43$$​​πr$$^3$$​

Volume of a cylinder: V= πr$$^2$$​h

The volume of the material is constant, so the volume of the sphere is equal to the volume of the cylinder.

Solution:

The radius (r) of both the sphere and the cylinder is half of the diameter.

r =$$\frac92$$​cm

Equate the volumes:

Since the solid ball is melted to form the cylinder, their volumes are equal.

Volume of Sphere = Volume of Cylinder

$$\frac 43$$​​πr$$^3$$=πr$$^2$$​h

$$\frac43$$​r = h

h=$$\frac43\times \frac 92$$​

h=6 cm

The height of the cylinder is 6 cm.