Question

practice 21.2
volume of pyramids
find the volume of each pyramid. round the result to the nearest tenth.

1. diagram of a pyramid with base 9, 12, height 10
2. diagram of a pyramid with base 6, 8, height 12
3. diagram of a pyramid with 12.5 mm, 15.2 mm, 8.1 mm
4. diagram of a square pyramid with base 12 in, 12 in, slant height 8 in?
5. diagram of a square pyramid with base 230 m, 230 m, slant height 146 m
6. diagram of a pyramid with base 1 m, height 1.5 m
7. find the volume of a hexagonal pyramid with a base area (b) of 25 ft² and a height of 9 ft.
8. find the volume of a hexagonal pyramid with a base area (b) of 36 ft² and a height of 11 ft.
9. find the volume of a square pyramid with a base edge of 45 feet and a height of 15 feet.
10. find the volume of a square pyramid with a base edge of 22 feet and a height of 17 feet.

find the volume of the composite figure. round to the nearest tenth.

1. diagram of a composite figure: a cube (12 cm, 12 cm, 12 cm) with a pyramid on top, height 18 cm

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Explanation:

Let's solve problem 7 first (hexagonal pyramid, base area \( B = 25 \, \text{ft}^2 \), height \( h = 9 \, \text{ft} \)):

The formula for the volume \( V \) of a pyramid is \( V = \frac{1}{3}Bh \), where \( B \) is the base area and \( h \) is the height.

Step 1: Identify the formula

The volume of a pyramid is given by \( V = \frac{1}{3}Bh \).

Step 2: Substitute the values

Here, \( B = 25 \, \text{ft}^2 \) and \( h = 9 \, \text{ft} \). Substitute these into the formula:
\[
V = \frac{1}{3} \times 25 \times 9
\]

Step 3: Calculate the volume

First, calculate \( 25 \times 9 = 225 \). Then, \( \frac{1}{3} \times 225 = 75 \).

Answer:

The volume of the hexagonal pyramid is \( 75 \, \text{cubic feet} \) (or \( 75 \, \text{ft}^3 \)).