What is the volume of a square-based pyramid with base side length of $8$ inches and a height of $12$ inches? Write your answer in the box provided. $\newline$ $\_\_\_\_\_ \text{in}^{3}.$

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Q. What is the volume of a square-based pyramid with base side length of

8

inches and a height of

12

inches? Write your answer in the box provided.

\newline

\_\_\_\_\_ \text{in}^{3}.

Calculate Base Area: To find the volume of a square-based pyramid, we use the formula: $\newline$ Volume = $(1/3) \times \text{base area} \times \text{height}$ $\newline$ First, we need to calculate the base area of the square pyramid. $\newline$ The base area of a square is found by squaring the side length. $\newline$ Base side length = $8$ inches $\newline$ Base area = $\text{side length} \times \text{side length}$
Calculate Volume: Now we calculate the base area: $\newline$ Base area = $8 \, \text{inches} \times 8 \, \text{inches}$ $\newline$ Base area = $64 \, \text{square inches}$
Evaluate Expression: Next, we use the volume formula for a square-based pyramid with the base area and the height: $\newline$ Volume = $(\frac{1}{3}) \times \text{base area} \times \text{height}$ $\newline$ Height = $12$ inches
Evaluate Expression: Next, we use the volume formula for a square-based pyramid with the base area and the height: $\newline$ Volume = $(\frac{1}{3}) \times \text{base area} \times \text{height}$ $\newline$ Height = $12$ inchesNow we calculate the volume: $\newline$ Volume = $(\frac{1}{3}) \times 64 \text{ square inches} \times 12 \text{ inches}$ $\newline$ Volume = $(\frac{1}{3}) \times 768 \text{ cubic inches}$
Evaluate Expression: Next, we use the volume formula for a square-based pyramid with the base area and the height: $\newline$ Volume = $(1/3) \times \text{base area} \times \text{height}$ $\newline$ Height = $12$ inchesNow we calculate the volume: $\newline$ Volume = $(1/3) \times 64 \text{ square inches} \times 12 \text{ inches}$ $\newline$ Volume = $(1/3) \times 768 \text{ cubic inches}$ Finally, we evaluate the expression to find the volume: $\newline$ Volume = $256 \text{ cubic inches}$