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.
- (a)(A) is true, (R) is false.
- (b)(A) is false, (R) is true.
- (c)Both (A) and (R) are true and (R) is the correct explanation of (A).
- (d)Both (A) and (R) are true, but (R) is not the correct explanation of (A).
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By formula,
Volume of sphere = $\frac{4}{3} \pi r^3$
Given,
A solid sphere is cut into two identical hemispheres.
Volume of hemisphere = $\frac{2}{3} \pi r^3$
Volume of two identical hemispheres = $2 \times \frac{2}{3} \pi r^3$
= $\frac{4}{3} \pi r^3$
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.