Exercise 12 Page 77

a We are asked to identify the shape of the top and bottom of a can of pineapple. To answer the question, let's draw the two-dimensional view of the top.

We can see above that the top view shows a circle and thus the top and bottom of the can have the shape of a circle.

b We are asked what shape we will get if we remove the top and the bottom, make a vertical cut down the side of the can, and uncurl and flatten the remaining body. Let's illustrate the situation with a diagram.

We can see above that the shape we get is a rectangle, where the base has the same length as the circumference of the top (and bottom) of the can, and the height is the same as the height of the can.

c We have to draw a net of the can labeling its dimensions. In part B, we drew a net without the top and bottom. Let's now draw a net of the can showing the top and the bottom, which are circles according to our answer to Part A.

We are told that the diameter of the can is

3

inches and the height is

2

inches. Let's find the circumference of the top (and bottom).

C = π \cdot d \Rightarrow C = π \cdot 3 \Leftrightarrow C = 3 π

We know from Part B that, in the net, the length of the base of the rectangle is the same as the circumference.

Subchapter links

Model and Analyze p.76-77