A solid sphere is cut into identical hemispheres.

Statement 1 : The total volume of two hemispheres is equal to the volume of the original sphere.

Statement 2 : The total surface area of two hemispheres together is equal to the surface area of the original sphere.

Which of the following is valid ?

1. Both the statements are true

2. Both the statements are false

3. Statement 1 is true, and statement 2 is false

4. Statement 1 is false, and statement 2 is true

When a solid sphere is cut into identical hemispheres.

Let radius of sphere be r.

Volume of a sphere = $\dfrac{4}{3}πr^3$

Volume of hemisphere = $\dfrac{2}{3}πr^3$

Volume of 2 hemisphere = $2 \times \dfrac{2}{3}πr^3 = \dfrac{4}{3}πr^3$.

The total volume of two hemispheres is equal to the volume of the original sphere.

Surface area of sphere = 4πr²

Surface area of hemisphere = 3πr²

Surface area of 2 hemisphere = 2 × 3πr² = 6πr².

The surface area of two hemispheres is not equal to the surface area of the original sphere.

Hence, Option 3 is the correct option.