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Find the volume of a pyramid with a square base, where the perimeter of the base is 12.3 in and the height of the pyramid is
8.9in. Round your answer to the nearest tenth of a cubic inch.
Answer: in
^(3)

Find the volume of a pyramid with a square base, where the perimeter of the base is $12$ . $3$ in and the height of the pyramid is $8.9 \mathrm{in}$ . Round your answer to the nearest tenth of a cubic inch. $\newline$ Answer: in $^{3}$

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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 perimeter of the base is

12

.

3

in and the height of the pyramid is

8.9 \mathrm{in}

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

\newline

Answer: in

^{3}

Calculate side length: Calculate the length of one side of the square base. $\newline$ Since the perimeter of the base is the sum of all four sides of the square, we divide the perimeter by $4$ to find the length of one side. $\newline$ Perimeter $= 4 \times \text{side\_length}$ $\newline$ $\text{side\_length} = \frac{\text{Perimeter}}{4}$ $\newline$ $\text{side\_length} = \frac{12.3 \, \text{in}}{4}$ $\newline$ $\text{side\_length} = 3.075 \, \text{in}$
Calculate base area: Calculate the area of the square base. $\newline$ The area of a square is found by squaring the length of one side. $\newline$ Area = $\text{side\_length}^2$ $\newline$ Area = $(3.075 \, \text{in})^2$ $\newline$ Area = $9.4565625 \, \text{in}^2$
Calculate volume: Calculate the volume of the pyramid. $\newline$ The volume of a pyramid is one-third the product of the base area and the height. $\newline$ Volume = $(\frac{1}{3}) \times \text{base\_area} \times \text{height}$ $\newline$ Volume = $(\frac{1}{3}) \times 9.4565625 \text{ in}^2 \times 8.9 \text{ in}$ $\newline$ Volume = $3$ . $1521875$ \text{ in}^ $2$ \times $8$ . $9$ \text{ in} $\newline$ Volume = $28$ . $05406875$ \text{ in}^ $3$
Round volume: Round the volume to the nearest tenth. $\newline$ Volume $\approx 28.1 \, \text{in}^3$

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