Question

A solid piece of wood shaped as a cylinder with an 8-centimeter diameter is cut as shown.



What is the surface area of the figure? Express the answer in terms of π.

96 + 64π cm2
96 + 80π cm2
96 + 112π cm2
96 + 128π cm2

Answer 1

Diameter = 8 so r = 4. Let the cylinder height be 12 (from the figure). After cutting along a plane through the axis we get a half–cylinder whose faces are:
- the flat rectangular cut: width = 8, height = 12, area = 8·12 = 96;
- the curved surface: half the full lateral area = (1/2)(2πrh) = πrh = π·4·12 = 48π;
- the two semicircular ends together = area of one full circle = πr^2 = 16π.

Total surface area = 96 + (48π + 16π) = 96 + 64π cm^2.

So the correct choice is 96 + 64π cm^2.