Match the given areas of various solid objects with their respective formulae:
| List I | List II | ||
|---|---|---|---|
| Area of solid object | Formula | ||
| (A) | Lateral surface area of a cylinder | (I) | \(\pi r\sqrt{r^2+h^2}\) |
| (B) | Total surface area of a hemisphere | (II) | \(4\pi r^2\) |
| (C) | Lateral surface area of a cone | (III) | \(2\pi rh\) |
| (D) | Surface area of a sphere | (IV) | \(3\pi r^2\) |
(Where, r = radius of the solid shape (or base) and h = height of the solid shape.)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
A lateral (curved) surface area leaves out the flat ends of a solid; a total surface area includes them.
(A) Lateral surface area of a cylinder — this matches (III) \(2\pi rh\). Cut open, the curved surface is a rectangle of length \(2\pi r\) (the base circumference) and breadth \(h\).
(B) Total surface area of a hemisphere — this matches (IV) \(3\pi r^2\). The curved part is half a sphere, \(2\pi r^2\), and the flat circular face adds \(\pi r^2\): \(2\pi r^2+\pi r^2=3\pi r^2\).
(C) Lateral surface area of a cone — this matches (I) \(\pi r\sqrt{r^2+h^2}\). It is \(\pi rl\), where the slant height \(l=\sqrt{r^2+h^2}\) by Pythagoras.
(D) Surface area of a sphere — this matches (II) \(4\pi r^2\), four times the area of a circle of the same radius.