Let's solve the problem step by step and explain the solution.
---
Problem:
We are given a
pyramid with the following information:
- The
height of the pyramid (from the apex to the base) is $ h = 9 $ cm.
- The
base of the pyramid is a triangle with:
- Base length $ b = 8 $ cm
- Height of the base triangle $ h_b = 5 $ cm
We are asked to find the
volume of the pyramid.
---
Step 1: Recall the Volume Formula for a Pyramid
The volume $ V $ of a pyramid is given by:
$$
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
$$
Where:
-
Base Area is the area of the base (in this case, a triangle),
-
Height is the perpendicular height from the apex to the base.
---
Step 2: Find the Area of the Base
The base is a triangle with:
- Base $ b = 8 $ cm
- Height $ h_b = 5 $ cm
Area of a triangle:
$$
\text{Base Area} = \frac{1}{2} \times b \times h_b = \frac{1}{2} \times 8 \times 5 = 20 \text{ cm}^2
$$
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Step 3: Plug into the Volume Formula
Now use the pyramid volume formula:
$$
V = \frac{1}{3} \times \text{Base Area} \times \text{Height} = \frac{1}{3} \times 20 \times 9
$$
$$
V = \frac{1}{3} \times 180 = 60 \text{ cm}^3
$$
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✔ Final Answer:
$$
\boxed{60} \text{ cm}^3
$$
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🔍 Explanation of the Given Solution in the Image:
The image shows:
$$
\text{Volume} = \frac{1}{3} \times \frac{1}{2}(8)(5)(9) = 60 \text{ cm}^3
$$
This is correct because:
- $ \frac{1}{2}(8)(5) $ computes the area of the triangular base,
- Then multiply by the height of the pyramid (9),
- Then divide by 3 (as per the pyramid volume formula).
So the calculation is:
$$
\frac{1}{3} \times \left( \frac{1}{2} \times 8 \times 5 \right) \times 9 = \frac{1}{3} \times 20 \times 9 = 60
$$
✔ Correct!
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📌 Summary:
- The base is a triangle with area $ 20 \text{ cm}^2 $
- The pyramid height is $ 9 $ cm
- Volume = $ \frac{1}{3} \times 20 \times 9 = 60 \text{ cm}^3 $
✔ Answer: $ \boxed{60} \text{ cm}^3 $
Parent Tip: Review the logic above to help your child master the concept of volume of triangular pyramid worksheet.
