Question : The total surface area of a cone whose radius is 3 cm and height is 4 cm is:
Option 1: $\frac{425}{7} \mathrm{~cm}^2$
Option 2: $\frac{501}{9} \mathrm{~cm}^2$
Option 3: $\frac{475}{8} \mathrm{~cm}^2$
Option 4: $\frac{528}{7} \mathrm{~cm}^2$
Correct Answer: $\frac{528}{7} \mathrm{~cm}^2$
Solution :
Radius ($r$) = 3 cm and height ($h$) = 4 cm
Let $l$ be the slant height of the cone.
We know, $l^2 = r^2 + h^2$
$⇒l^2 = 3^2 + 4^2$
$\therefore l= 5$ cm
$\therefore$ Total surface area $=\pi r(r+l)=\frac{22}{7} \times 3 \times(3+ 5)=\frac{528}{7}\ \text{cm}^2$
Hence the correct answer is $\frac{528}{7}\ \text{cm}^2$.
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