Find the total surface area of a cone, if its radius and slant height are 2r and 1/2 respectively.

Correct option is C

Given:

We are given that the radius r of a cone is 2r and the slant height l is $$\frac{1}{2}$$​ . We need to find the total surface area of the cone.

Formula Used:

The formula for the total surface area of a cone is:
​$$\text{Total Surface Area} = \pi R (R + L)$$​​
where R is the radius and L is the slant height.

Solution:

Substitute$$R = 2r \ and \ L = \frac{1}{2}$$​ into the formula:

​$$\text{Total Surface Area} = \pi (2r) \left(2r + \frac{1}{2}\right)$$​​

\$$\text{Total Surface Area} = \pi (2r) \times \left( \frac{4r +1}{2} \right)$$​​

​Total Surface Area = $$\pi r \times \left( {4r +1}{} \right)$$​​