Question

The surface area of a solid sphere is 120 square centimetre if its cut into2 halves what would be the surface area of each hemisphere?

Answer 1

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

                          Given Data :

• 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