Question : The radius of the base of a solid right circular cone is 8 cm and its height is 15 cm. The total surface area of the cone is:
Option 1: 200$\pi$
Option 2: 120$\pi$
Option 3: 136$\pi$
Option 4: 128$\pi$
Correct Answer: 200$\pi$
Solution :
Given:
Radius, $r\ = 8$ cm
Height, $h\ =\ 15$ cm
Let $l$ be the slant height.
As we know, $l^2\ =\ r^2\ +\ h^2$
$\Rightarrow l^2\ =\ 8^2\ +\ 15^2$
$\Rightarrow l^2\ =\ 64\ +\ 225$
$\Rightarrow l^2\ =\ 289$
$\therefore l\ =\ 17$ cm
Now,
Total Surface Area of the cone $=\pi r(r\ +\ l)\ =\ \pi\ \times 8 \times (8+ 17)\ =\ 200\pi$
Hence, the correct answer is $200\pi$.
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