Find the volume of a cylinder whose radius is one-third the radius of a circle of area 1386 cm², and height is twice its radius.

Correct option is C

Given:

The area of a circle is 1386 cm².
The radius of the cylinder is one-third the radius of the circle.
The height of the cylinder is twice its radius.

Formula Used:

The area of a circle is given by:
​$$A = \pi r^2$$​​
where  r  is the radius of the circle.
The volume of a cylinder is given by:
​$$V = \pi r^2 h$$​​
where ( r ) is the radius of the cylinder and ( h ) is its height.  

Solution:

Let the radius of circle be r

Area of the circle = $$πr^2=1386$$​​
​$$r^2= 1386×\frac{7}{22 } \\\ \\ r^2= 63×7 \\\ \\r = 21 cm.$$​​
Radius of cylinder = $$\frac{21}{3}$$​ = 7cm.
Height of the cylinder = 14 cm.
Therefore, volume of the cylinder = $$πr^2 h$$​​
= $$\frac{22}{7}×7×7×14$$​= 2156 cm³