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

1. 2πr(l + r)

2. $πr \Big(l + \dfrac{r}{4}\Big)$

3. πr(l + r)

4. 2πrl

Given,

Radius (R) = $\dfrac{r}{2}$,

Slant height (L) = 2l

Total surface area of cone (S) = πR(L + R)

Putting values we get,

$S = π \times \dfrac{r}{2} \times \Big(2l + \dfrac{r}{2}\Big) \\[1em] = \dfrac{πr}{2} \times 2l + \dfrac{πr}{2} \times \dfrac{r}{2} \\[1em] = πrl + \dfrac{πr^2}{4} \\[1em] = πr\Big(l + \dfrac{r}{4}\Big).$

Hence, Option 2 is the correct option.