Find the volume of a pyramid with a square base, where the side length of the base is $13$ . $2$ in and the height of the pyramid is $7.3 \mathrm{in}$ . Round your answer to the nearest tenth of a cubic inch. $\newline$ Answer: in $^{3}$

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

13

2

in and the height of the pyramid is

7.3 \mathrm{in}

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

\newline

Answer: in

^{3}

Calculate Base Area: The formula for the volume of a pyramid with a square base is $V = \frac{1}{3} \times \text{base\_area} \times \text{height}$ . The base area of a square is found by squaring the side length. So, we need to calculate the base area first. $\newline$ Base area = $\text{side\_length}^2 = 13.2 \, \text{in} \times 13.2 \, \text{in}$ .
Calculate Volume: Now, let's calculate the base area. $\newline$ Base area = $13.2 \, \text{in} \times 13.2 \, \text{in} = 174.24 \, \text{in}^2$ .
Round to Nearest Tenth: Next, we use the volume formula for the pyramid, substituting the base area and the height. $\newline$ Volume = $(\frac{1}{3}) \times \text{base\_area} \times \text{height} = (\frac{1}{3}) \times 174.24 \text{ in}^2 \times 7.3 \text{ in}$ .
Round to Nearest Tenth: Next, we use the volume formula for the pyramid, substituting the base area and the height. Volume = $(\frac{1}{3}) \times \text{base\_area} \times \text{height} = (\frac{1}{3}) \times 174.24 \text{ in}^2 \times 7.3 \text{ in}$ . Now, let's calculate the volume. Volume = $(\frac{1}{3}) \times 174.24 \text{ in}^2 \times 7.3 \text{ in} = 58.08 \text{ in}^2 \times 7.3 \text{ in} = 423.984 \text{ in}^3$ .
Round to Nearest Tenth: Next, we use the volume formula for the pyramid, substituting the base area and the height. $\newline$ Volume = $(\frac{1}{3}) \times \text{base\_area} \times \text{height} = (\frac{1}{3}) \times 174.24 \text{ in}^2 \times 7.3 \text{ in}$ .Now, let's calculate the volume. $\newline$ Volume = $(\frac{1}{3}) \times 174.24 \text{ in}^2 \times 7.3 \text{ in} = 58.08 \text{ in}^2 \times 7.3 \text{ in} = 423.984 \text{ in}^3$ .Finally, we round the volume to the nearest tenth of a cubic inch. $\newline$ Volume $\approx 424.0 \text{ in}^3$ (rounded to the nearest tenth).