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
    $2\pi\text{r}(\text{l+r})$
  • B
    $\pi\text{r}\Big(\text{l+}\frac{\text{r}}{4}\Big)$
  • C
    $\pi\text{r}(\text{l+r})$
  • D
    $2\pi\text{rl}$

Answer

  1. $\pi\text{r}\Big(\text{l+}\frac{\text{r}}{4}\Big)$

Solution:

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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