Consider the surface areas of the following solids:(A) A cuboid of 10…

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

Each solid’s total surface area is worked out with its own formula (taking \(\pi=\frac{22}{7}\)) and the four values are then compared.

(A) Cuboid 10 cm by 7 cm by 5 cm, surface area \(2(lb+bh+hl)\):

• Area of the six faces: \(2(70+35+50)=310\,\mathrm{cm}^{2}\)

(B) Cylinder of radius 3.5 cm and height 60 cm, surface area \(2\pi r(r+h)\):

• Curved surface and two ends: \(2\times\frac{22}{7}\times3.5\times63.5=1397\,\mathrm{cm}^{2}\)

(C) Cone of radius 6 cm and height 8 cm, surface area \(\pi r(r+l)\):

• Slant height from the right triangle of radius and height: \(l=\sqrt{36+64}=10\) cm

• Curved surface and base: \(\frac{22}{7}\times6\times16=301.7\,\mathrm{cm}^{2}\)

(D) Sphere of radius 12 cm, surface area \(4\pi r^{2}\):

• \(4\times\frac{22}{7}\times144=1810.3\,\mathrm{cm}^{2}\)

Tip: The order does not change if only the curved surfaces of the cylinder and the cone are taken (1320 and 188.6 cm²), so the question can be answered without worrying which area is meant.