Question

The total surface area of a cone whose radius is r/2 and slant height 2l is

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

Answer 1

The correct option is B

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

The correct option is (B)

The explanation for the correct options:

Given, that the radius of the cone is $\frac{\mathrm{r}}{2}$

The slant height is $2\mathrm{l}$

We have to find the total surface area of the cone.

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

Where, r is the radius of the cone, l is the slant height

Given, $\frac{\mathrm{r}}{2}$,$\mathrm{l}=2\mathrm{l}$

Total surface area $=\mathrm{\pi }\left(\frac{\mathrm{r}}{2}\right)(2\mathrm{l}+\frac{\mathrm{r}}{2})$

$=\pi \left[\right(\frac{r}{2}\left)\right(2l)+(\frac{r}{2}\left)\right(\frac{r}{2}\left)\right]$

$=\pi [rl+\frac{r^2}{4}]$

$=\mathrm{\pi r}(\mathrm{l}+\frac{\mathrm{r}}{4})$

Therefore, the total surface area is $=\mathrm{\pi r}(\mathrm{l}+\frac{\mathrm{r}}{4})$

The explanation for the incorrect options:

Option (A):

1. The given formula is incorrect with the arrived result.
2. Hence the incorrect answer is an option (A)

Option (C):

1. The Total surface area formula is$=\mathrm{\pi r}(\mathrm{l}+\mathrm{r})$.
2. The result is not matched with the arrival result.
3. Hence the incorrect answer is an option (C)

Option (D):

1. The Total surface area formula is$=2\mathrm{\pi rl}$.
2. The given formula is incorrect with the arrived result.
3. Hence the incorrect answer is an option (D)