Consider the surface areas of the following solids.
(A) A cuboid of 12 cm long, 7 cm broad, and 5 cm high.
(B) A cylinder of radius 3.5 cm and height 60 cm.
(C) A cone of radius 6 cm and height 8 cm.
(D) A sphere of radius 12.5 cm.
Arrange the above in decreasing order.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (D), (B), (A), (C)
The total surface area of each solid is worked out with its own formula and the four values are compared (\(\pi=\frac{22}{7}\)).
(A) Cuboid, 12 cm × 7 cm × 5 cm: \(2(lb+bh+hl)\)
Six rectangular faces, in three equal pairs: \(2(84+35+60)=2\times179=358\) cm2
(B) Cylinder, r = 3.5 cm, h = 60 cm: \(2\pi r(r+h)\)
Curved surface and two ends: \(\displaystyle 2\times\frac{22}{7}\times3.5\times63.5=22\times63.5=1397\) cm2
(C) Cone, r = 6 cm, h = 8 cm: slant height \(l=\sqrt{6^{2}+8^{2}}=10\) cm, area \(\pi r(l+r)\)
Curved surface and base: \(\displaystyle \frac{22}{7}\times6\times16\approx301.7\) cm2
(D) Sphere, r = 12.5 cm: \(4\pi r^{2}\)
One curved surface: \(\displaystyle 4\times\frac{22}{7}\times156.25\approx1964.3\) cm2