A pyramid has a square base. Each side of the base is 20 in. The height of the pyramid is 14 in. What is the volume of the pyramid?

Identify Formula for Volume: Identify the formula for the volume of a pyramid. The volume of a pyramid is given by the formula V = (1/3) * base area * height. Here, the base is a square with side length s = 20 inches, and the height h = 14 inches.Calculate Base Area: Calculate the area of the base. The area of a square base A = s^2, where s is the side length of the square. A = 20 inches * 20 inches = 400 square inches.Apply Volume Formula: Apply the volume formula using the area of the base and the height of the pyramid. Volume V = (1/3) * base area * height V = (1/3) * 400 square inches * 14 inchesPerform Multiplication: Perform the multiplication to find the volume. V = (1/3) * 400 * 14 V = (1/3) * 5600 V = 1866.666... cubic inchesRound Volume: Round the volume to a reasonable degree of precision. Since the problem does not specify the level of precision required, we can round to the nearest whole number. V ≈ 1867 cubic inches

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A pyramid has a square base. Each side of the base is $20\,\text{in}$ . The height of the pyramid is $14\,\text{in}$ . What is the volume of the pyramid?

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Grade 6

Volume of cubes and rectangular prisms: word problems

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Q. A pyramid has a square base. Each side of the base is

20\,\text{in}

. The height of the pyramid is

14\,\text{in}

. What is the volume of the pyramid?

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 is a square with side length $s = 20$ inches, and the height $h = 14$ inches.
Calculate Base Area: Calculate the area of the base. $\newline$ The area of a square base $A = s^2$ , where $s$ is the side length of the square. $\newline$ $A = 20 \text{ inches} \times 20 \text{ inches} = 400 \text{ square inches}.$
Apply Volume Formula: Apply the volume formula using the area of the base and the height of the pyramid. Volume $V = \frac{1}{3} \times$ base area $\times$ height $V = \frac{1}{3} \times 400$ square inches $\times 14$ inches
Perform Multiplication: Perform the multiplication to find the volume. $\newline$ $V = \frac{1}{3} \times 400 \times 14$ $\newline$ $V = \frac{1}{3} \times 5600$ $\newline$ $V = 1866.666\ldots$ cubic inches
Round Volume: Round the volume to a reasonable degree of precision. Since the problem does not specify the level of precision required, we can round to the nearest whole number. $V \approx 1867$ cubic inches