Find the volume of a pyramid with a square base, where the perimeter of the base is 4.2ft and the height of the pyramid is 4.7ft. Round your answer to the nearest tenth of a cubic foot. Answer: ft^(3)

Find Side Length: To find the volume of a pyramid with a square base, we need to know the length of a side of the base square and the height of the pyramid. The formula for the volume of a pyramid is V = (1/3) * base area * height. First, we need to find the length of a side of the base square using the perimeter. The perimeter (P) of a square is given by P = 4 * side length (s). Given P = 4.2 feet, we can solve for s. s = P / 4 s = 4.2 ft / 4 s = 1.05 ftCalculate Base Area: Now that we have the length of a side of the base square, we can find the area of the base (A). The area of a square is given by A = s^2. A = (1.05 ft)^2 A = 1.1025 ft^2Calculate Volume: With the base area and the height of the pyramid known, we can now calculate the volume (V). V = (1/3) * base area * height V = (1/3) * 1.1025 ft^2 * 4.7 ft V = 0.3675 ft^2 * 4.7 ft V = 1.72725 ft^3Round Final Answer: Finally, we round the answer to the nearest tenth of a cubic foot. V ≈ 1.7 ft^3

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Find the volume of a pyramid with a square base, where the perimeter of the base is
4.2ft and the height of the pyramid is
4.7ft. Round your answer to the nearest tenth of a cubic foot.
Answer:
ft^(3)

Find the volume of a pyramid with a square base, where the perimeter of the base is $4.2 \mathrm{ft}$ and the height of the pyramid is $4.7 \mathrm{ft}$ . Round your answer to the nearest tenth of a cubic foot. $\newline$ Answer: $\mathrm{ft}^{3}$

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Evaluate variable expressions: word problems

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

4.2 \mathrm{ft}

and the height of the pyramid is

4.7 \mathrm{ft}

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

\newline

Answer:

\mathrm{ft}^{3}

Find Side Length: To find the volume of a pyramid with a square base, we need to know the length of a side of the base square and the height of the pyramid. The formula for the volume of a pyramid is $V = (\frac{1}{3}) \times \text{base area} \times \text{height}$ . First, we need to find the length of a side of the base square using the perimeter. $\newline$ The perimeter ( $P$ ) of a square is given by $P = 4 \times \text{side length} (s)$ . Given $P = 4.2$ feet, we can solve for $s$ . $\newline$ $s = \frac{P}{4}$ $\newline$ $s = \frac{4.2 \text{ ft}}{4}$ $\newline$ $s = 1.05 \text{ ft}$
Calculate Base Area: Now that we have the length of a side of the base square, we can find the area of the base $A$ . The area of a square is given by $A = s^2$ . $A = (1.05 \, \text{ft})^2$ $A = 1.1025 \, \text{ft}^2$
Calculate Volume: With the base area and the height of the pyramid known, we can now calculate the volume $V$ .
$V = \frac{1}{3} \times \text{base area} \times \text{height}$
$V = \frac{1}{3} \times 1.1025 \, \text{ft}^2 \times 4.7 \, \text{ft}$
$V = 0.3675 \, \text{ft}^2 \times 4.7 \, \text{ft}$
$V = 1.72725 \, \text{ft}^3$
Round Final Answer: Finally, we round the answer to the nearest tenth of a cubic foot. $V \approx 1.7 \, \text{ft}^3$