Question

a container at a construction site is shaped like a rectangular prism. the container is 49 feet long, 45 feet wide, and 25 feet high. what is the volume of the container? use estimation to check the reasonableness of your answer. show your work.

Explanation:

Step1: Recall volume formula

The volume $V$ of a rectangular prism is given by $V = l\times w\times h$, where $l$ is the length, $w$ is the width and $h$ is the height.

Step2: Substitute values

Here, $l = 49$ feet, $w = 45$ feet and $h = 25$ feet. So $V=49\times45\times25$.
First, $49\times45=(50 - 1)\times45=50\times45-45=2250 - 45 = 2205$.
Then, $2205\times25=2205\times\frac{100}{4}=\frac{220500}{4}=55125$ cubic - feet.

Step3: Estimation for reasonableness

Estimate $49\approx50$, $45\approx50$ and $25\approx25$. Then $V\approx50\times50\times25 = 50\times1250=62500$. Since our calculated value of $55125$ is close to the estimated value of $62500$, the answer is reasonable.

Answer:

$55125$ cubic feet