Consider the surface area of the following:(A) A cube having each sid…

The correct answer is Option (1) → (B), (D), (C), (A)

Each surface area is worked out with its formula (taking \(\pi=\frac{22}{7}\)), and the four values are then placed from largest to smallest.

(A) A cube having each side as 6 cm — the smallest

• A cube has 6 square faces of area \(a^2\): surface area \(=6a^2=6\times36=216\,\mathrm{cm^2}\)

(B) A cylinder with a diameter of base 14 cm and length 80 cm — the largest

• The radius is half the diameter 14: \(r=7\)

• Curved surface \(=2\pi rh=2\times\frac{22}{7}\times7\times80=3520\,\mathrm{cm^2}\)

• Adding the two circular ends, each \(\pi r^2=154\): \(3520+308=3828\,\mathrm{cm^2}\)

(C) A cone of diameter 14 cm and a slant height of 10 cm

• The radius is half the diameter 14: \(r=7\)

• Curved surface \(=\pi rl=\frac{22}{7}\times7\times10=220\,\mathrm{cm^2}\)

• Adding the circular base, \(\pi r^2=154\): \(220+154=374\,\mathrm{cm^2}\)

(D) A sphere of radius 10.5 cm

• The surface of a sphere is \(4\pi r^2=4\times\frac{22}{7}\times10.5\times10.5=1386\,\mathrm{cm^2}\)

The order B, D, C, A is the same whether the curved or the total surface of the cylinder and the cone is taken.