A solid sphere is cut into two identical hemispheres.

Assertion (A): The total volume of two hemispheres is equal to the volume of the original sphere.

Reason (R): The total surface area of two hemispheres together is equal to the surface area of the original sphere.

1. (A) is true, (R) is false.

2. (A) is false, (R) is true.

3. Both (A) and (R) are true and (R) is the correct explanation of (A).

4. Both (A) and (R) are true, but (R) is not the correct explanation of (A).

By formula,

Volume of sphere = $\dfrac{4}{3} \pi r^3$

Given,

A solid sphere is cut into two identical hemispheres.

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

Volume of two identical hemispheres = $2 \times \dfrac{2}{3} \pi r^3$

= $\dfrac{4}{3} \pi r^3$

Thus, volume of a sphere = volume of two identical hemispheres.

So assertion (A) is true.

We know that,

Surface area of sphere = 4πr²

When a sphere is cut into two hemispheres, two new flat circular surfaces are created,

Surface area of a single hemisphere = Curved surface area + Area of its flat circular face

= 2πr² + πr²

= 3πr²

Total surface area of two hemispheres = 2 × 3πr² = 6πr².

Thus, surface area of a single hemisphere ≠ surface area of two hemispheres.

So reason (R) is false.

(A) is true, (R) is false.

Hence, option 1 is the correct option.