Question

The total surface area of a cone whose radius is $\frac{r}{2}$ and slant height $2l$ is

• A. $2\pi r(l+r)$
• B. $\pi r\left(l+\frac{r}{4}\right)$
• C. $\pi r(l+r)$
• D. $2\pi l$

Answer 1

The correct option is B

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

Step 1: Given data

Radius of cone$=\frac{r}{2}$

The slant height of a cone$=2l$

The total surface area of a cone $=?$

Step2: Calculating the total surface area of a cone

The total surface area of a cone$=\mathrm{\pi r}(r+l)$

The total surface area of a cone is given as,

$\mathrm{\pi r}(r+l)=\mathrm{\pi }\times \frac{r}{2}\left(\frac{r}{2}+2l\right)=\mathrm{\pi }\left(\frac{{\mathrm{r}}^2}{4}+\mathrm{rl}\right)=\mathrm{\pi r}\left(\frac{\mathrm{r}}{4}+\mathrm{l}\right)$

Hence, the total surface area of the cone will be$=\mathrm{\pi r}\left(\frac{\mathrm{r}}{4}+\mathrm{l}\right)$

Hence, option B is correct.