Question

You are making an umbrella that is shaped like a regular octagonal pyramid.

(a) Estimate the amount of fabric that you need to make the umbrella.

(b) The fabric comes in rolls that are 60 inches wide. Draw a diagram of how you can cut the fabric from rolls that are 10 feet long.

(c) How much fabric is wasted?

Answer 1

Hint:

Part (a) Given that :

Slant height $=5ft$

Side of octagon $=4ft$

Amount of fabric that we need to make the umbrella = total surface area of octagon

Total surface area of octagon $=8\times \frac{1}{2}\times 5\times 4f{t}^2$

Total surface area of octagon $=80f{t}^2$

Part (c) Width of fabric roll = 60 inches

Width of fabric roll $=\frac{60}{12}ft$

$=5ft$

Length of fabric roll $=10ft$

Total surface area of fabric roll $=5\times 10f{t}^2$

Total surface area of fabric roll $=50f{t}^2$