Let's solve each pyramid volume problem step by step.
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Formula for the Volume of a Pyramid:
$$
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
$$
We'll apply this formula to each pyramid.
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a) First Pyramid
- Base: A
rectangle with dimensions:
- Length = 2 cm
- Width = 2 cm
- Height of the pyramid (vertical height from base to apex) =
9 cm
#### Step 1: Find the base area
$$
\text{Base Area} = \text{length} \times \text{width} = 2 \, \text{cm} \times 2 \, \text{cm} = 4 \, \text{cm}^2
$$
#### Step 2: Apply the volume formula
$$
V = \frac{1}{3} \times 4 \times 9 = \frac{36}{3} = 12 \, \text{cm}^3
$$
✔ Volume = 12 cm³
---
b) Second Pyramid
- Base: A
triangle with:
- Base = 6 cm
- Height of triangle = 2 cm
- Height of the pyramid (from apex to base plane) =
4 cm
#### Step 1: Find the base area (area of triangle)
$$
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 2 = 6 \, \text{cm}^2
$$
#### Step 2: Apply the volume formula
$$
V = \frac{1}{3} \times 6 \times 4 = \frac{24}{3} = 8 \, \text{cm}^3
$$
✔ Volume = 8 cm³
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c) Third Pyramid
- Base: A
rectangle with:
- Length = 12 cm
- Width = 3 cm
- Height of the pyramid =
10 cm
#### Step 1: Find the base area
$$
\text{Base Area} = 12 \times 3 = 36 \, \text{cm}^2
$$
#### Step 2: Apply the volume formula
$$
V = \frac{1}{3} \times 36 \times 10 = \frac{360}{3} = 120 \, \text{cm}^3
$$
✔ Volume = 120 cm³
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✔ Final Answers:
a)
12 cm³
b)
8 cm³
c)
120 cm³
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Let me know if you'd like a visual explanation or help with any other geometry problems!
Parent Tip: Review the logic above to help your child master the concept of volume of triangular pyramid worksheet.
