Question

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.

विकल्प

• (A) is true, (R) is false.

• (A) is false, (R) is true.

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

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

Answer 1

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

Explanation:

By formula,

Volume of sphere = `4/3 πr^3`

Given,

A solid sphere is cut into two identical hemispheres.

Volume of hemisphere = `2/3 πr^3`

Volume of two identical hemispheres = `2 xx 2/3 πr^3`

= `4/3 πr^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, the surface area of a single hemisphere ≠ the surface area of two hemispheres.

So reason (R) is false.