MCQ
Write the correct answer in the following: The total surface area of a cone whose radius is $\frac{\text{r}}{2}$ and slant height 2l is:
  • A
    $2\pi\text{r}(\text{l+r})$
  • $\pi\text{r}\Big(\text{l+}\frac{\text{r}}{4}\Big)$
  • C
    $\pi\text{r}(\text{l+r})$
  • D
    $2\pi\text{rl}$

Answer

Correct option: B.
$\pi\text{r}\Big(\text{l+}\frac{\text{r}}{4}\Big)$
Total surface area of cone $=$ Area of the base $+$ Curved Surface area of cone
$=\pi\Big(\frac{\text{r}}{2}\Big)^2+\pi\Big(\frac{\text{r}}{2}\Big)\times2\text{l}=\frac{\pi\text{r}}{2}\Big(\frac{\text{r}}{2}+2\text{l}\Big)$
$=\frac{\pi\text{r}}{4}(\text{r}+4\text{l})=\pi\text{r}\Big(\text{l}+\frac{\text{r}}{4}\Big)$
Hence, $(b)$ is the correct answer.

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