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Find the volume of a pyramid with a square base, where the area of the base is
19.9m^(2) and the height of the pyramid is
21.5m. Round your answer to the nearest tenth of a cubic meter.
Answer:
m^(3)

Find the volume of a pyramid with a square base, where the area of the base is $19.9 \mathrm{~m}^{2}$ and the height of the pyramid is $21.5 \mathrm{~m}$ . Round your answer to the nearest tenth of a cubic meter. $\newline$ Answer: $\mathrm{m}^{3}$

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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 area of the base is

19.9 \mathrm{~m}^{2}

and the height of the pyramid is

21.5 \mathrm{~m}

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

\newline

Answer:

\mathrm{m}^{3}

Identify formula for volume: Identify the formula for the volume of a pyramid. $\newline$ The volume of a pyramid is given by the formula $V = \frac{1}{3} \times \text{base area} \times \text{height}$ . $\newline$ Here, the base area ( $A$ ) is $19.9 \, \text{m}^2$ and the height ( $h$ ) is $21.5 \, \text{m}$ .
Substitute given values: Substitute the given values into the formula. $\newline$ Volume = $(\frac{1}{3}) \times 19.9 \, \text{m}^2 \times 21.5 \, \text{m}$
Perform multiplication: Perform the multiplication to find the volume. $\newline$ Volume = $(\frac{1}{3}) \times 19.9 \times 21.5$ $\newline$ Volume = $(\frac{1}{3}) \times 426.85 \, \text{m}^3$
Calculate final volume: Calculate the final volume by dividing by $3$ . $\newline$ Volume = $426.85 \, \text{m}^3 / 3$ $\newline$ Volume = $142.2833\ldots \, \text{m}^3$
Round answer: Round the answer to the nearest tenth of a cubic meter. $\newline$ Volume $\approx 142.3$ m $^3$

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