The solid and the Surface area (S.A) of the following solids are give…

The correct answer is Option (3) → (A), (C)

Note: The given answer is as per the official NTA Answer Key. However, statement (C) is correct only if “S.A” is read as the curved surface area of the cylinder; its total surface area is 3828 cm², as explained below. NTA’s cylinder in (C) has come without its two round lids.

Each statement is checked by working out the surface area of the solid from its standard formula (\(\pi=\frac{22}{7}\)).

(A) A cube of edge 9 cm., S.A = 486 cm² Correct. A cube has six equal square faces.

• Six faces, each \(9\times9\) cm: S.A \(=6a^{2}=6\times81=486\) cm²

(B) A cuboid of 18 cm. long, 14 cm. width and 7 cm. height, S.A = 108 cm² Incorrect. A cuboid has three pairs of equal rectangular faces.

• Two faces each of \(18\times14\), \(14\times7\) and \(7\times18\): S.A \(=2(lb+bh+hl)=2(252+98+126)\)

• Total of the six faces: S.A \(=2\times476=952\) cm², not 108 cm²

(C) A cylinder with diameter of 14 cm. and height 80 cm., S.A = 3520 cm² Correct as per NTA; however, 3520 cm² is only the curved surface area. The value 3520 cm² is the curved surface area of the cylinder, \(2\pi rh\).

• Radius is half the diameter: \(r=\frac{14}{2}=7\) cm

• Curved surface area \(\displaystyle=2\times\frac{22}{7}\times7\times80=3520\) cm²

• With the two circular ends (\(2\pi r^{2}=308\) cm²) the total surface area would be 3828 cm²

(D) A sphere with radius of 14 cm., S.A = 2004 cm² Incorrect. The surface area of a sphere is \(4\pi r^{2}\).

• With radius 14 cm: S.A \(\displaystyle=4\times\frac{22}{7}\times14\times14=2464\) cm², not 2004 cm²