Consider the surface area of the following solids.
A. A cube of edge 9 cm.
B. A cuboid of edges 18 cm, 14 cm and 7 cm.
C. A cylinder with radius of 14 cm and height 80 cm.
D. A sphere with radius of 14 cm.
Arrange the above in decreasing order.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → C, D, B, A
Each surface area is worked out with its own formula (taking \(\pi=\frac{22}{7}\)), and the four values are then put in decreasing order.
The cube (A), with 6 square faces: \(6a^{2}=6\times81=486\,\mathrm{cm^{2}}\)
The cuboid (B), with three pairs of faces: \(2(18\times14+14\times7+7\times18)=952\,\mathrm{cm^{2}}\)
The cylinder (C), curved surface and two ends: \(\displaystyle 2\pi r(r+h)=2\times\frac{22}{7}\times14\times94=8272\,\mathrm{cm^{2}}\)
The sphere (D): \(\displaystyle 4\pi r^{2}=4\times\frac{22}{7}\times196=2464\,\mathrm{cm^{2}}\)
So C (8272) > D (2464) > B (952) > A (486). The order stays the same even if only the curved surface of the cylinder is taken (\(2\pi rh=7040\,\mathrm{cm^{2}}\)).