Match List-I with List-II.
| List-I | List-II | ||
|---|---|---|---|
| A. | Volume of frustum | I. | \(2\pi(R+r)h+2\pi(R^2-r^2)\) |
| B. | Total surface area of hollow cylinder | II. | (Side) \(\times\sqrt{3}\) |
| C. | Diagonal of a cube | III. | \(\displaystyle\frac{1}{3}\pi(R^2+r^2+Rr)h\) |
| D. | Volume of pyramid | IV. | \(\displaystyle\frac{1}{3}\times\) Area of base \(\times\) height |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A-III, B-I, C-II, D-IV
Each solid is matched with the formula that fits its shape; the letters R and r stand for two different radii.
A. Volume of frustum — this matches III. \(\frac{1}{3}\pi(R^2+r^2+Rr)h\). A frustum is a cone with its top cut off parallel to the base, so it has two circular ends of radii R and r, and its volume uses both.
B. Total surface area of hollow cylinder — this matches I. \(2\pi(R+r)h+2\pi(R^2-r^2)\). It is the outer curved surface \(2\pi Rh\), the inner curved surface \(2\pi rh\), and the two ring-shaped ends, each of area \(\pi(R^2-r^2)\).
C. Diagonal of a cube — this matches II. (Side) \(\times\sqrt{3}\). For a cube of side a, the diagonal is \(\sqrt{a^2+a^2+a^2}=a\sqrt{3}\).
D. Volume of pyramid — this matches IV. \(\frac{1}{3}\times\) Area of base \(\times\) height. A pyramid holds one-third of the prism with the same base and height, just as a cone holds one-third of its cylinder.