Consider the surface area of the following solids.(A) A cube of edge…

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

Note: The given answer is as per the official NTA Answer Key. However, the question has two possible answers, i.e. both Option (4) and Option (3), as explained below.

The order of (A) and (C) depends on whether the curved surface or the total surface of the hemisphere (and of the cylinder) is taken; \(\pi=\frac{22}{7}\) throughout.

Taking the curved surfaces, the order is (D), (B), (A), (C), Option (4):

• Cube of edge 8 cm, \(6a^{2}\): (A) \(6\times64=384\) cm²

• Cylinder, curved surface \(2\pi rh\): (B) \(2\times\frac{22}{7}\times5\times42=1320\) cm²

• Hemisphere, curved surface \(2\pi r^{2}\): (C) \(2\times\frac{22}{7}\times49=308\) cm²

• Sphere, \(4\pi r^{2}\): (D) \(4\times\frac{22}{7}\times441=5544\) cm²

Taking the total surface areas, the usual meaning of the surface area of a solid (a solid hemisphere also has its flat circular face), the order is (D), (B), (C), (A), Option (3):

• Cube: (A) 384 cm², as above

• Cylinder, \(2\pi r(r+h)\): (B) \(2\times\frac{22}{7}\times5\times47\approx1477.1\) cm²

• Hemisphere, \(3\pi r^{2}\): (C) \(3\times\frac{22}{7}\times49=462\) cm², now more than the cube

• Sphere: (D) 5544 cm², as above

Tip for students: When a question has two possible answers, mark the one you worked out yourself. If NTA’s answer key gives a different answer, challenge it when NTA opens the window for challenges.