Find the volume of a pyramid with a square base, where the perimeter of the base is $13.1 \mathrm{ft}$ and the height of the pyramid is $6.7 \mathrm{ft}$ . Round your answer to the nearest tenth of a cubic foot. $\newline$ Answer: $\mathrm{ft}^{3}$

View step-by-step help

Home

Math Problems

Grade 7

Convert between customary and metric systems

Full solution

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

13.1 \mathrm{ft}

and the height of the pyramid is

6.7 \mathrm{ft}

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

\newline

Answer:

\mathrm{ft}^{3}

Find Side Length: First, we need to find the length of one side of the square base. Since the perimeter of a square is the sum of all its sides, and a square has four equal sides, we divide the perimeter by $4$ . $\newline$ Perimeter of the base = $13.1\,\text{ft}$ $\newline$ Length of one side of the base = Perimeter $\div 4$ $\newline$ Length of one side of the base = $13.1\,\text{ft} \div 4$
Calculate Area: Now, let's calculate the length of one side of the base. $\newline$ Length of one side of the base = $13.1 \, \text{ft} \div 4$ $\newline$ Length of one side of the base = $3.275 \, \text{ft}$ $\newline$ We will round this to the nearest tenth later if necessary.
Calculate Volume: Next, we calculate the area of the square base using the length of one side. $\newline$ Area of the base = (Length of one side) $\newline$ Area of the base = $(3.275 \, \text{ft})^2$
Round Volume: Let's perform the calculation for the area of the base. $\newline$ Area of the base = $(3.275 \, \text{ft})^2$ $\newline$ Area of the base = $10.726625 \, \text{ft}^2$ $\newline$ We will round this to the nearest tenth later if necessary.
Round Volume: Let's perform the calculation for the area of the base. $\newline$ Area of the base = $(3.275 \, \text{ft})^2$ $\newline$ Area of the base = $10.726625 \, \text{ft}^2$ $\newline$ We will round this to the nearest tenth later if necessary.Now we can calculate the volume of the pyramid. The formula for the volume of a pyramid with a square base is: $\newline$ Volume = $(\text{Area of the base} \times \text{Height}) \div 3$ $\newline$ Volume = $(10.726625 \, \text{ft}^2 \times 6.7 \, \text{ft}) \div 3$
Round Volume: Let's perform the calculation for the area of the base. $\newline$ Area of the base = $(3.275 \, \text{ft})^2$ $\newline$ Area of the base = $10.726625 \, \text{ft}^2$ $\newline$ We will round this to the nearest tenth later if necessary.Now we can calculate the volume of the pyramid. The formula for the volume of a pyramid with a square base is: $\newline$ Volume = $(\text{Area of the base} \times \text{Height}) \div 3$ $\newline$ Volume = $(10.726625 \, \text{ft}^2 \times 6.7 \, \text{ft}) \div 3$ Let's perform the calculation for the volume of the pyramid. $\newline$ Volume = $(10.726625 \, \text{ft}^2 \times 6.7 \, \text{ft}) \div 3$ $\newline$ Volume = $71.8683875 \, \text{ft}^3 \div 3$ $\newline$ Volume = $23.95612917 \, \text{ft}^3$
Round Volume: Let's perform the calculation for the area of the base. $\newline$ Area of the base = $(3.275 \, \text{ft})^2$ $\newline$ Area of the base = $10.726625 \, \text{ft}^2$ $\newline$ We will round this to the nearest tenth later if necessary.Now we can calculate the volume of the pyramid. The formula for the volume of a pyramid with a square base is: $\newline$ Volume = $\frac{\text{Area of the base} \times \text{Height}}{3}$ $\newline$ Volume = $\frac{10.726625 \, \text{ft}^2 \times 6.7 \, \text{ft}}{3}$ Let's perform the calculation for the volume of the pyramid. $\newline$ Volume = $\frac{10.726625 \, \text{ft}^2 \times 6.7 \, \text{ft}}{3}$ $\newline$ Volume = $\frac{71.8683875 \, \text{ft}^3}{3}$ $\newline$ Volume = $23.95612917 \, \text{ft}^3$ Finally, we round the volume to the nearest tenth of a cubic foot as requested. $\newline$ Volume \approx $24.0 \, \text{ft}^3$