Question : The perimeter of the base of a right circular cone is 132 cm. If the height of the cone is 72 cm, then What is the total surface area (in cm2) of the cone?
Option 1: 6600
Option 2: 6336
Option 3: 4224
Option 4: 5784
Correct Answer: 6336
Solution :
The perimeter of the base of a right circular cone is the circumference of the base, where $r$ is the radius of the base is $2\pi r$.
$⇒132=2\pi r$
$⇒r = \frac{132}{2\pi} = 21\;\text{cm}$
$⇒l = \sqrt{r^2 + h^2}$
$⇒l = \sqrt{21^2 + 72^2} = 75\;\text{cm}$
The total surface area of a cone, where $l$ is the slant height of the cone $ =\pi r (r + l)$
The total surface area of a cone $= \frac{22}{7} \times 21 \times (21 + 75) = 6336\;\mathrm{cm^2}$
Hence, the correct answer is 6336.
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