Absolutely! Let's solve each problem step by step. The goal is to find the
volume of a square base pyramid using the formula:
>
Volume = (1/3) × Base Area × Height
Since the base is a
square, the
Base Area = side².
So, the full formula becomes:
>
Volume = (1/3) × (side)² × height
We’ll apply this to each pyramid.
---
Problem 1:
- Base edge = 7 cm
- Height = 9 cm
Working Out:
Base Area = 7² = 49 cm²
Volume = (1/3) × 49 × 9
= (1/3) × 441
=
147 cm³
✔ Answer: 147 cm³
---
Problem 2:
- Base edge = 3½ in = 3.5 in
- Height = 5 in
Working Out:
Base Area = (3.5)² = 12.25 in²
Volume = (1/3) × 12.25 × 5
= (1/3) × 61.25
=
20.4167 in³ (or as a fraction: 61.25 ÷ 3 = 245/12 ≈ 20 5/12 in³)
✔ Answer: 20.42 in³ (rounded to two decimal places) or
245/12 in³
---
Problem 3:
- Base edge = 2.3 m
- Height = 4.5 m
Working Out:
Base Area = (2.3)² = 5.29 m²
Volume = (1/3) × 5.29 × 4.5
= (1/3) × 23.805
=
7.935 m³
✔ Answer: 7.94 m³ (rounded to two decimal places)
---
Problem 4:
- Base edge = 7.6 cm
- Height = 10 cm
Working Out:
Base Area = (7.6)² = 57.76 cm²
Volume = (1/3) × 57.76 × 10
= (1/3) × 577.6
=
192.533... cm³
✔ Answer: 192.53 cm³ (rounded to two decimal places)
---
Problem 5:
- Base edge = 6 in
- Height = 9½ in = 9.5 in
Working Out:
Base Area = 6² = 36 in²
Volume = (1/3) × 36 × 9.5
= (1/3) × 342
=
114 in³
✔ Answer: 114 in³
---
##
✔ Final Answers Summary:
| Pyramid | Working Out | Volume |
|---------|--------------------------------------|---------------|
| 1 | (1/3) × 7² × 9 = (1/3) × 49 × 9 |
147 cm³ |
| 2 | (1/3) × (3.5)² × 5 = (1/3) × 12.25 × 5 |
20.42 in³ |
| 3 | (1/3) × (2.3)² × 4.5 = (1/3) × 5.29 × 4.5 |
7.94 m³ |
| 4 | (1/3) × (7.6)² × 10 = (1/3) × 57.76 × 10 |
192.53 cm³|
| 5 | (1/3) × 6² × 9.5 = (1/3) × 36 × 9.5 |
114 in³ |
---
📌
Note for Students: Always remember:
- Square base → area = side × side
- Pyramid volume = 1/3 × base area × height
- Units are cubed (cm³, in³, m³) because it’s volume!
Let me know if you’d like to see the fraction versions or step-by-step long division for any of them!
Parent Tip: Review the logic above to help your child master the concept of volume of pyramids worksheet.
