Question

Emily convinced her mom to buy a giant box of her favorite cereal. Her mom doesn't think the box will fit on their shelf. The volume of the box is
\[10{,}000\] cm
\[^3\]. The base of the box is
\[25\] cm by
\[10\] cm.
How tall is the box of cereal?

Answer 1

To find the height of the box of cereal, we need to use the formula for the volume of a rectangular box:

\[
\text{Volume} = \text{Base Area} \times \text{Height}
\]

We are given the volume of the box as \( 10,000 \, \text{cm}^3 \) and the dimensions of the base as \( 25 \, \text{cm} \) (length) and \( 10 \, \text{cm} \) (width).

First, we calculate the area of the base:

\[
\text{Base Area} = \text{Length} \times \text{Width} = 25 \, \text{cm} \times 10 \, \text{cm} = 250 \, \text{cm}^2
\]

Now, we can plug in the volume and the base area into the volume formula to find the height:

\[
10,000 \, \text{cm}^3 = 250 \, \text{cm}^2 \times \text{Height}
\]

To find the height, we can rearrange the formula:

\[
\text{Height} = \frac{\text{Volume}}{\text{Base Area}} = \frac{10,000 \, \text{cm}^3}{250 \, \text{cm}^2}
\]

Now, we perform the division:

\[
\text{Height} = \frac{10,000}{250} = 40 \, \text{cm}
\]

Thus, the height of the box of cereal is

\[
\boxed{40 \, \text{cm}}
\]