Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (Figures, etc.) | (Area/Volume/Diagonal etc.) | ||
| (A) | Surface area of Cube | (I) | \(\pi(R^2-r^2)\) |
| (B) | Volume of Right pyramid | (II) | \(a\sqrt{2}\) |
| (C) | Area of Circular Ring | (III) | \(6a^2\) |
| (D) | Diagonal of Square | (IV) | \(\displaystyle\frac{1}{3}\) (area of base) × 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)-(IV), (C)-(I), (D)-(II)
Each measure in List-I is matched with its formula, where \(a\) is a side, \(R\) and \(r\) are radii.
(A) Surface area of Cube — this matches (III) \(6a^2\). A cube has six square faces, each of area \(a^2\).
(B) Volume of Right pyramid — this matches (IV) \(\frac{1}{3}\) (area of base) × height. A pyramid holds one-third of the prism with the same base and height.
(C) Area of Circular Ring — this matches (I) \(\pi(R^2-r^2)\). The ring is the outer circle with the inner circle removed: \(\pi R^2-\pi r^2\).
(D) Diagonal of Square — this matches (II) \(a\sqrt{2}\). The diagonal is the hypotenuse of a right triangle with both legs \(a\): \(\sqrt{a^2+a^2}=a\sqrt{2}\).