What is the total surface area of a cone whose radius is $\frac{r}{4}$ and slant height is $4l$?

The formula for the Total Surface Area ($\text{TSA}$) of a cone is given by:
$$\text{TSA}=\pi \times \text{radius}\times (\text{slant height}+\text{radius})$$

Given:

* $\text{Radius}=\frac{r}{4}$
* $\text{Slant height}=4l$

Substitute these values into the formula:

$$\text{TSA}=\pi \left(\frac{r}{4}\right)\left(4l+\frac{r}{4}\right)$$

Now, distribute $\frac{1}{4}$ inside the bracket:

$$\text{TSA}=\pi r\left(\frac{4l}{4}+\frac{r}{4\times 4}\right)$$

$$\text{TSA}=\pi r\left(l+\frac{r}{16}\right)$$

Therefore, the total surface area of the cone is $\pi r\left(l+\frac{r}{16}\right)$.