Multiple choice

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

  1. $\pi 2r (l + r) $
  2. $\pi r \left (l + \dfrac{r}{4}\right)$
  3. $\pi r (l + r) $
  4. $2\pi rl$
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B Correct answer
Explanation

Total surface area of a cone = pi * radius * (slant height + radius). Given radius = r/2 and slant height = 2l. Area = pi * (r/2) * (2l + r/2) = pi * r * (l + r/4).

AI explanation

The total surface area of a cone is given by the formula πrl + πr^2, where r is the radius and l is the slant height. Substituting the given values, r = r/2 and l = 2l, the area becomes π(r/2)(2l) + π(r/2)^2. Simplifying this expression results in πrl + π(r^2/4), which can be factored as πr(l + r/4).

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