Question : The radius of a right circular cone is 3 cm and its height is 4 cm. The total surface area of a cone is:
Option 1: 48.4 cm2
Option 2: 64.4 cm2
Option 3: 96.4 cm2
Option 4: 75.4 cm2
Correct Answer: 75.4 cm 2
Solution :
The total surface area of a right circular cone of radius $r$ and slant height $l$ is $\pi r (r + l)$.
Given: $r = 3 \, \text{cm}$ and $h = 4 \, \text{cm}$.
$⇒l = \sqrt{r^2 + h^2}$
$⇒l = \sqrt{3^2 + 4^2} = 5 \, \text{cm}$
The total surface area of a right circular cone $= \pi r (r + l)$
where \(r\) is the radius of the base of the cone and \(l\) is the slant height of the cone.
The total surface area of a right circular cone $= \frac{22}{7}\times 3 \, \text{cm} \times (3 \, \text{cm} + 5 \, \text{cm}) $
The total surface area of a right circular cone $= 75.4 \, \text{cm}^2$
Hence, the correct answer is 75.4 cm
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