Question

a shipping container is in the form of a right rectangular prism, with dimensions of 25 ft by 8 ft by 9 ft 6 in. how many cubic feet of shipped goods would it hold when its three - quarters full? round your answer to the nearest tenth if necessary.

Explanation:

Step1: Convert inches to feet

Since \(1\) foot \( = 12\) inches, then \(6\) inches \(=\frac{6}{12}=0.5\) feet. So the height of the container is \(h = 9.5\) feet.

Step2: Calculate the volume of the container

The volume \(V\) of a right - rectangular prism is given by the formula \(V=l\times w\times h\), where \(l = 25\) feet, \(w = 8\) feet, and \(h=9.5\) feet.

$$V=25\times8\times9.5$$

$$V = 200\times9.5$$

$$V=1900$$

cubic feet.

Step3: Calculate the volume when it is three - quarters full

If the container is three - quarters full, then the volume \(V_{full}\) of the goods is \(V_{full}=\frac{3}{4}\times V\).
Substitute \(V = 1900\) into the formula:

$$V_{full}=\frac{3}{4}\times1900$$

$$V_{full}=3\times475$$

$$V_{full}=1425$$

Answer:

\(1425\) cubic feet.