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Find the volume of a pyramid with a square base, where the side length of the base is 18.5 in and the height of the pyramid is 10.9 in. Round your answer to the nearest tenth of a cubic inch.

Find the volume of a pyramid with a square base, where the side length of the base is $18$ . $5$ in and the height of the pyramid is $10$ . $9$ in. Round your answer to the nearest tenth of a cubic inch.

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Volume of cubes and rectangular prisms: word problems

Full solution

Q. Find the volume of a pyramid with a square base, where the side length of the base is

18

.

5

in and the height of the pyramid is

10

.

9

in. Round your answer to the nearest tenth of a cubic inch.

Identify Formula: Step $1$ : Identify the formula for the volume of a pyramid. The formula is $\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}$ . Here, the base is a square with side length $18.5$ in.
Calculate Base Area: Step $2$ : Calculate the area of the square base. Area = $\text{side length} \times \text{side length} = 18.5 \, \text{in} \times 18.5 \, \text{in} = 342.25 \, \text{in}^2$ .
Plug Area and Height: Step $3$ : Plug the area and height into the volume formula. Volume = $(\frac{1}{3}) \times 342.25 \text{ in}^2 \times 10.9 \text{ in}$ .
Find Volume: Step $4$ : Perform the multiplication and division to find the volume. Volume = $(\frac{1}{3}) \times 342.25 \times 10.9 = 1242.2825$ in³. Round this to the nearest tenth: $1242.3$ in³.

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\newline

1

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