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 ?
- (a)Both the statements are true
- (b)Both the statements are false
- (c)Statement 1 is true, and statement 2 is false
- (d)Statement 1 is false, and statement 2 is true
Show SolutionHide Solution↓
When a solid sphere is cut into identical hemispheres.
Let radius of sphere be r.
Volume of a sphere = $\frac{4}{3}πr^3$
Volume of hemisphere = $\frac{2}{3}πr^3$
Volume of 2 hemisphere = $2 \times \frac{2}{3}πr^3 = \frac{4}{3}πr^3$.
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.