Question

A surface area of a solid sphere is 120 square centimeters.If it is cut into two halves what would be the surface area of each hemisphere?

Answer 1

                                                $\huge{\underline{\mathfrak{Surface\:Area}}}$

                                              Given Data :

1. The total surface area of the sphere is 120 cm²

Let us take the radius of the solid sphere as r.

Then, the surface area of the sphere would be 4πr² cm².

The surface area is given as 120 cm².

So, 4πr² = 120 cm²

Which implies, r²=  $\frac{30}{pi}$  ------ (1)

We know that, curved surface area of the hemisphere is $\frac{1}{2}$  × 4πr² = πr².

Base area = πr²

Now the total surface of the hemisphere will be 2πr² + πr² = 3πr²

Let us substitute the value from -- (1)

The total surface area of each hemisphere = 3πr × $\frac{30}{pi}$

                      = 90 cm²

Answer 2

SOLUTION:-

Given:

A surface area of a solid sphere is 120cm².If it is cut into two halves.

To find:

The surface area of each hemisphere.

Explanation:

We have,

• A surface area of solid sphere is 120cm².

We know that, formula of the surface area of the sphere: 4πr²

Here,

⇒ 4πr²=120

⇒ πr²= 120/4

⇒ πr²= 30

⇒ r²= 30/π..................(1)

Now,

Formula: Surface area of hemisphere: 2πr²

We have base area= πr²

Total surface area of the hemisphere= 3πr².

Using the equation (1) place of r²

$3\pi * \frac{30}{\pi } \\\\3*30\\\\90$

Thus,

The total surface area of each hemisphere is 90cm².