Question
Jayden has a box that is 3 feet high, 2 feet wide, and 4 feet long. What is the volume of the box?
Answer:
The base area of a box is 48 inches and the height is 14 inches. What is the volume of the box?
Answer:
The volume of a box is 288 centimeters. The length of the box is 12 centimeters and the height is 6 centimeters. What is the width of the box?
Answer:
Answers
GPT-4o mini
To find the volumes and dimensions of the boxes, we will use the formula for the volume of a rectangular box:
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
1. **For Jayden's box**:
- Height = 3 feet
- Width = 2 feet
- Length = 4 feet
\[
\text{Volume} = 4 \, \text{feet} \times 2 \, \text{feet} \times 3 \, \text{feet} = 24 \, \text{cubic feet}
\]
**Answer:** 24 cubic feet
---
2. **For the second box**:
- Base area = 48 square inches
- Height = 14 inches
To find the volume, we can use the formula:
\[
\text{Volume} = \text{Base Area} \times \text{Height} = 48 \, \text{inches}^2 \times 14 \, \text{inches} = 672 \, \text{cubic inches}
\]
**Answer:** 672 cubic inches
---
3. **For the third box**:
- Volume = 288 cubic centimeters
- Length = 12 centimeters
- Height = 6 centimeters
We need to find the width. Rearranging the volume formula gives:
\[
\text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}} = \frac{288 \, \text{cm}^3}{12 \, \text{cm} \times 6 \, \text{cm}}
\]
Calculating the denominator:
\[
12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2
\]
Now substituting back:
\[
\text{Width} = \frac{288 \, \text{cm}^3}{72 \, \text{cm}^2} = 4 \, \text{cm}
\]
**Answer:** 4 centimeters
\[
\text{Volume} = \text{length} \times \text{width} \times \text{height}
\]
1. **For Jayden's box**:
- Height = 3 feet
- Width = 2 feet
- Length = 4 feet
\[
\text{Volume} = 4 \, \text{feet} \times 2 \, \text{feet} \times 3 \, \text{feet} = 24 \, \text{cubic feet}
\]
**Answer:** 24 cubic feet
---
2. **For the second box**:
- Base area = 48 square inches
- Height = 14 inches
To find the volume, we can use the formula:
\[
\text{Volume} = \text{Base Area} \times \text{Height} = 48 \, \text{inches}^2 \times 14 \, \text{inches} = 672 \, \text{cubic inches}
\]
**Answer:** 672 cubic inches
---
3. **For the third box**:
- Volume = 288 cubic centimeters
- Length = 12 centimeters
- Height = 6 centimeters
We need to find the width. Rearranging the volume formula gives:
\[
\text{Width} = \frac{\text{Volume}}{\text{Length} \times \text{Height}} = \frac{288 \, \text{cm}^3}{12 \, \text{cm} \times 6 \, \text{cm}}
\]
Calculating the denominator:
\[
12 \, \text{cm} \times 6 \, \text{cm} = 72 \, \text{cm}^2
\]
Now substituting back:
\[
\text{Width} = \frac{288 \, \text{cm}^3}{72 \, \text{cm}^2} = 4 \, \text{cm}
\]
**Answer:** 4 centimeters