Answer: B
Assume the radius of both the right circular cylinder and the hemisphere is \(r\) units, and the height of the cylinder is \(h\) units. Now, the height of the hemisphere is equal to its radius, which is \(r\) units. - Volume of the cylinder = \(\pi r^2 h\) cubic units - Volume of the hemisphere = \(\dfrac{2}{3} \pi r^3\) cubic units According to the question, \[\pi r^2 h = \dfrac{2}{3} \pi r^3\] Dividing both sides by \(\pi r^2\): \[h = \dfrac{2}{3} r \Rightarrow r = \dfrac{3}{2} h\] So, the height of the hemisphere is greater than the height of the cylinder by: \[ \frac{r - h}{h} \times 100\% = \frac{\dfrac{3}{2}h - h}{h} \times 100\% = \frac{\dfrac{h}{2}}{h} \times 100\% = 50\% \]
Assume the radius of both the right circular cylinder and the hemisphere is \(r\) units, and the height of the cylinder is \(h\) units. Now, the height of the hemisphere is equal to its radius, which is \(r\) units. - Volume of the cylinder = \(\pi r^2 h\) cubic units - Volume of the hemisphere = \(\dfrac{2}{3} \pi r^3\) cubic units According to the question, \[\pi r^2 h = \dfrac{2}{3} \pi r^3\] Dividing both sides by \(\pi r^2\): \[h = \dfrac{2}{3} r \Rightarrow r = \dfrac{3}{2} h\] So, the height of the hemisphere is greater than the height of the cylinder by: \[ \frac{r - h}{h} \times 100\% = \frac{\dfrac{3}{2}h - h}{h} \times 100\% = \frac{\dfrac{h}{2}}{h} \times 100\% = 50\% \]