To find the volume of a square-based pyramid, you can use the formula:
\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
- Calculate the base area: The base is a square, so the area \( A \) of the base is given by:
\[ A = \text{side}^2 \]
Since each edge of the base measures 8 centimeters:
\[ A = 8 \times 8 = 64 \text{ cm}^2 \]
- Determine the height: The problem does not specify the height (h) of the pyramid. If we are to assume a height or know it from additional information provided (e.g., through a diagram or description), we can proceed. For calculation purposes, if the height were given, you should just plug that value into the volume formula.
Supposing we have a common scenario where the height is equal to the length of a side, we can proceed using h = 8 cm. However, if not specified, we cannot compute without further information.
Let’s assume the height \( h \) is provided or if it's another common value (like the height that meets the geometry of a typical square-based pyramid), you can use h = 8 cm for our calculations.
So:
\[ V = \frac{1}{3} \times 64 \text{ cm}^2 \times 8 \text{ cm} \]
Calculating this gives us:
\[ V = \frac{1}{3} \times 512 \text{ cm}^3 = \frac{512}{3} \text{ cm}^3 \approx 170.67 \text{ cm}^3 \]
- Rounding: Finally, round 170.67 to the nearest whole number:
\[ V \approx 171 \text{ cm}^3 \]
In this analysis, the height needs to be solidified for the specific problem you’re addressing. If other values are involved, including a specific height, please provide that, and I can assist you further!
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