Consider the surface area of the following solids.
A. A cube of edge 4 cm.
B. A cylinder with a diameter of base 14 cm and height 35 cm.
C. A hemisphere with 28 cm diameter.
D. A sphere with a radius 7 cm.
Arrange the above in decreasing order and choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → B, C, D, A
The surface area of a solid is the total area of all its faces, flat and curved. Each one is worked out with \(\pi=\frac{22}{7}\).
A. Cube of edge 4 cm (six equal square faces):
Its total surface area: \(6a^{2}=6\times16=96\,\mathrm{cm^2}\)
B. Cylinder, \(r=7\) cm, \(h=35\) cm (curved surface and two circular ends):
Its total surface area: \(2\pi r(r+h)=2\times\frac{22}{7}\times7\times42=1848\,\mathrm{cm^2}\)
C. Hemisphere, \(r=14\) cm (curved part \(2\pi r^{2}\) and the flat circle \(\pi r^{2}\)):
Its total surface area: \(3\pi r^{2}=3\times\frac{22}{7}\times196=1848\,\mathrm{cm^2}\)
D. Sphere, \(r=7\) cm:
Its total surface area: \(4\pi r^{2}=4\times\frac{22}{7}\times49=616\,\mathrm{cm^2}\)
B and C have the same surface area, 1848 cm2, so they share the top place, followed by D and then A. Only Option (3) puts B and C ahead of D and A. If only the curved surfaces of B and C are taken (1540 cm2 and 1232 cm2), B comes before C and the order is again B, C, D, A.