# dimensions of the prism

A rect. prism has a length of (l), a width of (w), and a height of 1. Volume of the rect prism is 24cm3. Use your knowledge of volume and surface area to derive a function F(W) that represents the surface area of the rect. prism in terms of its width.

Next, graph it on calculator.

Lastly, find the dimensions of the prism to the nearest tenth of a centimeter that will minimize the quantity of material needed to manufacture the can.

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#### Solution Preview

The formula for the volume of a rectangular prism is V = l w h. Given a volume of 24 cm3 and a height of 1, we get

24 = lw. This will allow us to write the length in terms of the width by dividing both sides by w. This gives l = 24 / w.

The surface area of a rectangular prism is S.A. = 2B + ph where B is the area of a base, p is the perimeter of the base, and h is the height. Let's ...

#### Solution Summary

This solution finds the dimensions of the prism to the nearest tenth of a centimeter.