Question

if the radius and length of a cone are r/2 and 2l respectively what is the total surface area

Answer 1

TSA OF CONE =PIE ×R (L+R)
=PIE ×R/2 (2L+R/3)

Answer 2

Answer: Total surface area of the cone is $\frac{\pi r}{4}(r+\sqrt{r^2+16l^2})$

Step-by-step explanation:

Since we have given that

Radius of a cone is given by

$\frac{r}{2}$

Length of a cone = 2l

So, Slant height of cone is given by

$l=\sqrt{r^2+h^2}\\\\l=\sqrt{\frac{r}{2}^2+(2l)^2}\\\\l=\sqrt{\frac{r^2}{4}+4l^2}\\\\l=\sqrt{\frac{r^2+16l^2}{4}}\\\\l=\frac{\sqrt{r^2+16l^2}}{2}$

As we know the formula for "Total surface area of cone":

$Area=\pi r(r+l)\\\\Area=\pi \times \frac{r}{2}(\frac{r}{2}+\frac{\sqrt{r^2+16l^2}}{2})\\\\Area=\frac{\pi r}{4}(r+\sqrt{r^2+16l^2})$

Hence, Total surface area of the cone is $\frac{\pi r}{4}(r+\sqrt{r^2+16l^2})$