A cone, a hemisphere and a cylinder stand on equal bases and have the same height. What is the ratio of their volumes?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 1 : 2 : 3
For same base and height of Cone, cylinder and hemisphere,
height of cone and cylinder, h = radius of hemisphere, r = base radius of cone and cylinder, rb
Volume of Cone V1= \(\frac{1}{3}\)π \( {rb}^{2} \) h = \(\frac{1}{3}\)π \( {r}^{3} \)
Volume of hemisphere V2= \(\frac{2}{3}\)π \( {r}^{3} \) = \(\frac{2}{3}\)π \( {r}^{3} \)
Volume of Cylinder V3= π \( {rb}^{2} \) h = π \( {r}^{3} \)
V1:V2:V3 :: \(\frac{1}{3}\) : \(\frac{2}{3}\) : 1 = 1:2:3