Calculate the total surface area of a cone if its radius is $$\frac{r}{4}$$​ and slant Height is $$4l$$​.

Correct option is C

Given:

Radius of cone $$= \frac{r}{4}$$​​
Slant height of cone = 4l

Formula Used:
Total Surface Area (TSA) of a cone = Curved Surface Area + Base Area

Curved Surface Area = πrl

Base Area = $$\pi r^2$$​​

TSA = $$\pi r l + \pi r^2 = \pi r(l + r)$$​

Solution:
Substitute r =$$\frac{r}{4}, l = 4l:$$​​

Curved Surface Area = $$\pi \cdot \frac{r}{4} \cdot 4 = \pi r l$$​​

Base Area $$= \pi \left(\frac{r}{4}\right)^2 = \pi \cdot \frac{r^2}{16}$$​​

​$$\text{TSA} = \pi r l + \frac{\pi r^2}{16} \\ \ \\ = \pi r(l +\frac{r}{16})$$

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