Question : The perimeter of the base of a right circular cone is 44 cm. If the height of the cone is 24 cm, then what is the curved surface area (in cm2) of the cone?
Option 1: 550
Option 2: 1100
Option 3: 2200
Option 4: 650
Correct Answer: 550
Solution :
The perimeter of the base of a right circular cone is given as 44 cm.
The circumference of the base = $2\pi r$, where $r$ is the radius of the base.
$⇒2\pi r=44$
$⇒r = \frac{44}{2\pi}=\frac{22}{\pi}=\frac{22×7}{22}=7\;\mathrm{cm}$
$⇒l = \sqrt{r^2 + h^2}$
$⇒l = \sqrt{(7\;\mathrm{cm})^2 + (24\;\mathrm{cm})^2}$
$⇒l=25\;\mathrm{cm}$
The curved surface area of a cone $ = \pi rl$
The curved surface area of a cone = $\frac{22}{7}$ × 7 × 25
The curved surface area of a cone = 550 cm
2
Hence, the correct answer is 550.
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