Match List I with List II
| List I | List II | ||
|---|---|---|---|
| A. | Volume of cone | I. | \(\displaystyle\frac{1}{3}\pi h\left(r_1^2+r_2^2+r_1r_2\right)\) |
| B. | Volume of sphere | II. | \(\displaystyle\frac{1}{3}\pi r^2h\) |
| C. | Volume of frustum | III. | \(\pi r^2h\) |
| D. | Volume of cylinder | IV. | \(\displaystyle\frac{4}{3}\pi r^3\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → A-II, B-IV, C-I, D-III
(A) Volume of cone — this matches (II) \(\displaystyle\frac{1}{3}\pi r^2h\). A cone holds one-third of a cylinder of the same base and height.
(B) Volume of sphere — this matches (IV) \(\displaystyle\frac{4}{3}\pi r^3\). A sphere has only a radius, so its volume depends on the radius alone, through \(r^3\).
(C) Volume of frustum — this matches (I) \(\displaystyle\frac{1}{3}\pi h\left(r_1^2+r_2^2+r_1r_2\right)\). A frustum is a cone with its top cut off, so it has two radii, one for each circular face.
(D) Volume of cylinder — this matches (III) \(\pi r^2h\). It is the area of the circular base times the height.