Question

1. cereal boxes come in various sizes. for example, the family - sized box has dimensions of 24 cm by 33 cm by 11.5 cm and the regular - sized box has dimensions of 19.7 cm by 30.5 cm by 9.5 cm.

a. what is the capacity of each of these boxes of cereal?

Explanation:

Step1: Calculate family - sized box capacity

The volume formula for a rectangular prism (box) is $V = l\times w\times h$. For the family - sized box, $l = 24$ cm, $w=33$ cm, $h = 11.5$ cm. So $V_1=24\times33\times11.5$.
$V_1 = 24\times33\times11.5=24\times379.5 = 9108$ $cm^3$.

Step2: Calculate regular - sized box capacity

For the regular - sized box, $l = 19.7$ cm, $w = 30.5$ cm, $h=9.5$ cm. Using the volume formula $V = l\times w\times h$, we have $V_2=19.7\times30.5\times9.5$.
$V_2=19.7\times30.5\times9.5 = 19.7\times289.75=5708.075$ $cm^3$.

Answer:

The capacity of the family - sized box is $9108$ $cm^3$ and the capacity of the regular - sized box is $5708.075$ $cm^3$.