Word Problem Involving Functions

[sunstar2882]

A skating rink is in the shape of a rectangle with semicircles at the ends. The length of the rectangle is 20 feet less than twice the width. The thickness of the ice is .75 inches.

a) Build a model that expresses the ice volume V as a function of the width.

b) How much ice is in the rink if the width is 90 feet?


I was able to draw a picture for (a) but I was unsure of how to write a formula with V as a function of the width. My teacher said we should write a formula.

Any insight would be appreciated!

 

[tkhunny]

#1 - Name Stuff

W = Width of Rectangle.
L = Length of Rectangle
R = Radius of semi-circles

Do you see these?

Total Area: \(\displaystyle W\cdot L + 2\cdot\frac{\pi R^{2}}{2}\)

Okay, now you need to translate the additional information.

1) How does R relate to W?
2) How does L relate to W?

You're almost done.