If r represents the radius and h denotes the height of the solid. Then, Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| Solid | Volume | ||
| (A) | Cylinder | (I) | \(\frac{2}{3}\pi r^{3}\) |
| (B) | Cone | (II) | \(\frac{4}{3}\pi r^{3}\) |
| (C) | Sphere | (III) | \(\frac{1}{3}\pi r^{2}h\) |
| (D) | Hemisphere | (IV) | \(\pi r^{2}h\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-IV, B-III, C-II, D-I
Solids with a flat circular base and a height have \(r^{2}h\) in their volume; the sphere and the hemisphere, which have no separate height, have \(r^{3}\).
(A) Cylinder — this matches (IV) \(\pi r^{2}h\). Its volume is the area of the circular base, \(\pi r^{2}\), times the height.
(B) Cone — this matches (III) \(\frac{1}{3}\pi r^{2}h\). A cone holds one-third of a cylinder with the same base and height.
(C) Sphere — this matches (II) \(\frac{4}{3}\pi r^{3}\), the standard volume of a sphere of radius \(r\).
(D) Hemisphere — this matches (I) \(\frac{2}{3}\pi r^{3}\). A hemisphere is half a sphere: \(\frac{1}{2}\times\frac{4}{3}\pi r^{3}=\frac{2}{3}\pi r^{3}\).