Consider the surface area of the following solids.(A) A cylinder with…

The correct answer is Option (4) → (A), (D), (C), (B)

Note: The given answer is as per the official NTA Answer Key. However, the answer given by NTA holds only if the curved surface areas are compared. For solids, surface area usually means the total surface area, and with total surface areas the order is (D), (A), (C), (B), which is not among the options, as explained below. NTA painted only the curved parts of these solids and left the flat faces unpainted.

The order (A), (D), (C), (B) comes from comparing the curved surface areas of the four solids, that is, the area of the curved surface of each, leaving out its flat ends or base. Keeping \(\pi\) as a common factor:

• Cylinder (A), radius 7 cm, curved surface \(2\pi rh\): \(2\pi\times7\times80=1120\pi\) cm²

• Cone (B), slant height 10 cm, curved surface \(\pi rl\): \(\pi\times7\times10=70\pi\) cm²

• Sphere (C), surface \(4\pi r^{2}\): \(4\pi\times49=196\pi\) cm²

• Hemisphere (D), curved surface \(2\pi r^{2}\): \(2\pi\times441=882\pi\) cm²

In decreasing order: \(1120\pi>882\pi>196\pi>70\pi\), that is (A), (D), (C), (B).

With total surface areas (the curved surface together with the flat ends or base):

• Cylinder (A): \(2\pi r(r+h)=2\pi\times7\times87=1218\pi\) cm²

• Cone (B): \(\pi r(l+r)=\pi\times7\times17=119\pi\) cm²

• Sphere (C): \(196\pi\) cm² (a sphere has no flat face)

• Hemisphere (D): \(3\pi r^{2}=3\pi\times441=1323\pi\) cm²

The hemisphere now comes first, giving (D), (A), (C), (B), which no option offers.