Question

The surface area of a sphere is 616 sqm. The surface area of its hemisphere is
A. 205.6 cm
B. 308 cm
C. 1232 cm
D. 38 cm​

Answer 1

The CSA of hemispher is 308cm

Answer 2

The surface area of its hemisphere is option (B): 308 cm².

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Correct Question:

The surface area of a sphere is 616 sq cm. The surface area of its hemisphere is

A. 205.6 cm²

B. 308 cm²

C. 1232 cm²

D. 38 cm²​

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Let's understand a few concepts:

To calculate the surface area of the hemisphere of the given sphere we will use the following formulas:

$\boxed{\bold{Total\: Surface \:Area \:of\:Sphere = 4\pi r^2}}$

$\boxed{\bold{Curved \:Surface \:Area \:of\:Hemisphere = 2\pi r^2}}$

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Let's solve the given problem:

The surface area of the sphere = 616 cm²

By using the above formula of the total surface area of the sphere, we get

$4\pi r^2 = 616$

$\implies r^2 = \frac{616}{4\pi }$

$\implies r^2 = \frac{616}{4\times \frac{22}{7} }$

$\implies r^2 = \frac{616\times 7}{4\times 22 }$

$\implies r^2 = \frac{616\times 7}{88 }$

$\implies r^2 = 7 \times 7$

$\implies r = 7\:m$

Here we have to calculate the surface area of the sphere's hemisphere, so we must find the curved surface area of the hemisphere.

Therefore,

The curved surface area of the hemisphere is,

= $2\pi r^2$

= $2\times \frac{22}{7} \times 7^2$

= $2\times 22 \times 7$

= $\bold{308\:cm^2}$ ← option (B)

Thus, the surface area of its hemisphere is 308 cm².

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