Match the given areas of various solid objects with their respective formulae:

(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:

(A)-(III), (B)-(IV), (C)-(I), (D)-(II)

The correct answer is Option (1) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)

(A) Lateral Surface Area of a Cylinder: The lateral (curved) surface of a cylinder is found by multiplying the circumference of the base ($2\pi r$) by the height ($h$). Formula: $2\pi rh$ → Matches with (III)

(B) Total Surface Area of a Hemisphere: A hemisphere has a curved surface area ($2\pi r^2$) and a flat circular base ($\pi r^2$). The total surface area is the sum of both: $2\pi r^2 + \pi r^2 = 3\pi r^2$. Formula: $3\pi r^2$ → Matches with (IV)

(C) Lateral Surface Area of a Cone: The lateral surface area is given by $\pi r l$, where $l$ is the slant height. The slant height can be calculated using the Pythagorean theorem as $l = \sqrt{r^2 + h^2}$. Formula: $\pi r \sqrt{r^2 + h^2}$ → Matches with (I)

(D) Surface Area of a Sphere: The total surface area of a sphere is exactly four times the area of its circular cross-section. Formula: $4\pi r^2$ → Matches