If a wooden right circular cylinder with radius 2 meters and height 6 meters has a cylindrical hole of diameter 2 meters drilled through the center as shown, what is the entire surface area (including the top and bottom faces), in square meters, of the resulting figure ?

Options

A. `38 pi`
B. `40pi`
C. `42pi`
D. `44pi`

Answer

C

Explanation

The entire surface area you're looking for consists of the lateral areas of the outside cylinder and the inside cylinder, plus the areas of the larger top and bottom circles, minus the areas of the smaller top and bottom circles. The lateral area of the outside cylinder is `2pi rh = 2pi (3)(6)=24pi`. The lateral area of the inside cylinder is `2pi rh = 2pi (1)(6)=12pi`. The areas of the larger top and bottom circles are each `pi r^(2) = pi (2^(2))=4pi`. And the areas of the smaller top and bottom circles are each `pi r^(2)=pi(1^(2))=pi`. The total surface area, then, is
`24pi + 12pi + 2(4pi)-2(pi)=42(pi)`