Let's solve each problem step by step using the formula for the
volume of a rectangular prism:
$$
\text{Volume} = \text{length} \times \text{width} \times \text{height}
$$
---
Problem 1:
- Given:
- Length = 6 cm
- Width = $ a $ cm
- Height = 6 cm
- Volume = 288 cm³
Use the volume formula:
$$
6 \times a \times 6 = 288
$$
$$
36a = 288
$$
$$
a = \frac{288}{36} = 8
$$
✔ Answer: $ a = 8 $ cm
---
Problem 2:
- Dimensions:
- Length = 2.5 ft
- Width = 6 ft
- Height = 3 ft
$$
\text{Volume} = 2.5 \times 6 \times 3 = 45 \text{ ft}^3
$$
✔ Answer: Volume = $ 45 $ ft³
---
Problem 3:
- Given:
- Length = 6 in
- Width = 5 in
- Height = $ b $ in
- Volume = 90 in³
$$
6 \times 5 \times b = 90
$$
$$
30b = 90
$$
$$
b = \frac{90}{30} = 3
$$
✔ Answer: $ b = 3 $ in
---
Problem 4:
- Given:
- Length = 2 cm
- Width = 4 cm
- Height = $ c $ cm
- Volume = 28 cm³
$$
2 \times 4 \times c = 28
$$
$$
8c = 28
$$
$$
c = \frac{28}{8} = 3.5
$$
✔ Answer: $ c = 3.5 $ cm
---
Problem 5:
- Dimensions:
- Length = 9 in
- Width = 7.5 in
- Height = 2 in
$$
\text{Volume} = 9 \times 7.5 \times 2
$$
First: $ 9 \times 7.5 = 67.5 $
Then: $ 67.5 \times 2 = 135 $
✔ Answer: Volume = $ 135 $ in³
---
Problem 6:
- Dimensions:
- Length = 10 m
- Width = 3 m
- Height = 1.5 m
$$
\text{Volume} = 10 \times 3 \times 1.5 = 30 \times 1.5 = 45 \text{ m}^3
$$
✔ Answer: Volume = $ 45 $ m³
---
✔ Final Answers Summary:
1. $ a = 8 $ cm
2. Volume = $ 45 $ ft³
3. $ b = 3 $ in
4. $ c = 3.5 $ cm
5. Volume = $ 135 $ in³
6. Volume = $ 45 $ m³
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of volume rectangular prism worksheet answers.
