Question

If the total surface area of a solid hemisphere is $12\pi {cm}^2$, then its curved surface are is equal to

• A. $6\pi {cm}^2$
• B. $24\pi {cm}^2$
• C. $36\pi {cm}^2$
• D. $8\pi {cm}^2$

Answer 1

The correct option is D $8\pi {cm}^2$

Given, the total surface area of the hemisphere $=12\pi c{m}^2$.

We know that the total surface area of a hemisphere $=3\pi r^2$.

Hence, $3\pi r^2=12\pi$

$\Rightarrow r^2=4$

$\therefore r=2cm$

Now, we know that the curved surface area of the hemisphere $=2\pi r^2$.

Hence, curved surface area $=2\pi \times 2^2$

$\Rightarrow 8\pi c{m}^2$

Hence, the curved surface area of the solid hemisphere is $8\pi c{m}^2$.