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:

Area of the circle = 1386 cm².

Let the radius of the circle be r .

Formula Used:

Area of circle = $$\pi r^2$$​​

Volume of cylinder =$$\pi r^2 h$$​​

Solution:

Area of circle =$$\pi r^2$$​​

Substituting the value of the area:

1386 = $$\pi r^2$$​​

Solving for r :

r =$$\sqrt{\frac{1386}{\pi}} = 21 \, \text{cm}$$​​

Now, the radius of the cylinder is one-third of the radius of the circle:

Radius of cylinder =$$\frac{21}{3} = 7 \, \text{cm}$$​​

The height of the cylinder is twice its radius:

Height of cylinder = $$2 \times 7 = 14 \, \text{cm}$$​​

The formula for the volume of the cylinder is:

Volume =$$\pi r^2 h$$​​

Substituting the values:

Volume = $$\pi \times 7^2 \times 14 = 2156 \, \text{cm}^3$$​​

Thus, the volume of the cylinder is approximately 2156 cm³.