Question

A container built for transatlantic shipping is constructed in the shape of a right rectangular prism. Its dimensions are 11 ft by 5.5 ft by 11.5 ft. The container is entirely full. If, on average, its contents weigh 0.45 pounds per cubic foot, and, on average, the contents are worth $4.72 per pound, find the value of the container’s contents. Round your answer to the nearest cent.

Answer 1

Value of container's contents = $1477.77

Explanation:

Step 1: Find the volume of the container:

First, we need to find the volume of the container before we can find the weight in pounds. The formula for volume of a right rectangular prism is given by:

V = lwh, where

• V is the volume in cubic feet,
• l is the length,
• w is the width,
• and h is the height.

Thus, we can plug in 11 for l, 5.5 for w, and 11.5 for h in the volume formula to find V, the volume of the container in the shape of a right rectangular prism:

V = (11)(5.5)(11.5)

V = (60.5)(11.5)

V = 695.75

Thus, the volume of the container is 695.75 cubic feet.

Step 2: Determine the weight of the container's contents:

Since we're told that normally the contents weigh 0.45 pounds per cubic foot, we can determine the weight of 695.75 cubic feet by creating a proportion to solve for w, the weight:

0.45 pounds / 1 cubic foot = w pounds / 695.75 cubic feet

0.45 = w/695.75

0.45 * 695.75 = w

313.0875 = w (Let's not round at this intermediate step and wait to to round at the end)

Thus, the weight of 695.75 cubic feet is 313.0875 pounds.

Step 3: Determine the price of 313.09 pounds:

Finally, we can determine the price, p, of 313.0875 pounds by making another proportion:

$4.72 / 1 pound = $p / 313.0875 pounds

4.72 = p / 313.0875

313.0875 * 4.72 = p

1477.773 = p

1477.77 = p

Thus, the cost of 313.09 pounds is about $1477.77.