Question

A solid right circular cylinder is made with clay whose diameter is 4 cm and height is 48 cm. Reema wants to make number of spheres of diameter 4 cm. How many solid spheres can be made out of it?

Answer 1

Given:

A solid right circular cylinder is made with clay whose diameter is 4 cm and height is 48 cm.

Reema wants to make a number of spheres of diameter 4 cm.

To find:

How many solid spheres can be made out of it?

Solution:

The dimensions of the solid right circular cylinder:

The diameter = 4 cm

So,the radius, r = $\frac{diameter}{2} = \frac{4}{2} = 2\:cm$

The height, h = 48 cm

∴ The volume of the solid right circular cylinder  is,

= Volume of a cylinder

= $\pi r^2 h$  

= $\pi (2)^2 (48)$

 

The dimension of each sphere:

The diameter = 4 cm

So, the radius, r = $\frac{diameter}{2} = \frac{4}{2} = 2\:cm$

∴ The volume of each sphere = $\frac{4}{3} \pi r^3 = \frac{4}{3} \pi (2)^3$

 

Now,

The required no. of solid spheres that can be made from the solid right circular cylinder is,

= $\frac{Volume \:of\:cylinder}{Volume\:of\:each\:sphere}$  

= $\frac{\pi (2)^2 (48)}{ \frac{4}{3} \pi (2)^3}$

 = $\frac{ (48)}{ \frac{4}{3} \times (2)}$

= $\frac{ 48\times 3}{ 4 \times 2}$

= 18

 

Thus, 18 solid spheres can be made out of the solid right circular cylinder.

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