Questions: Joel wanted a large box of cereal, but his mom was unsure if it would fit in the pantry. The box had a volume of 6900 cm 3 , a base length of 23 cm , and a depth of 10 cm . What was the height of the box?

Joel wanted a large box of cereal, but his mom was unsure if it would fit in the pantry. The box had a volume of 6900 cm 3 , a base length of 23 cm , and a depth of 10 cm . What was the height of the box?

Transcript text: Joel wanted a large box of cereal, but his mom was unsure if it would fit in the pantry. The box had a volume of 6900 cm 3 , a base length of 23 cm , and a depth of 10 cm . What was the height of the box? Answer: $\square$

Solution

Solution Steps

Step 1: Understand the Problem

We are given the volume of a cereal box and its base dimensions. We need to find the height of the box. The volume $ V $ of a rectangular box is given by the formula:

\[ V = \text{length} \times \text{depth} \times \text{height} \]

Step 2: Substitute Known Values

We know the volume $ V = 6900 \, \text{cm}^3 $, the base length is $ 23 \, \text{cm} $, and the depth is $ 10 \, \text{cm} $. Substituting these values into the volume formula, we have:

\[ 6900 = 23 \times 10 \times \text{height} \]

Step 3: Solve for the Height

To find the height, we need to solve the equation for the height:

\[ 6900 = 230 \times \text{height} \]

Divide both sides by 230 to isolate the height:

\[ \text{height} = \frac{6900}{230} \]

Calculate the height:

\[ \text{height} = 30 \]