Question

Arturo sketches this square-based pyramid. Each edge of the base measures 8 centimeters, as shown in the image. What is the volume of Arturo's pyramid, rounded to the nearest whole cubic centimeter? (1 point) Ο 640 214 Ο 27 213

Answer 1

To find the volume of a square-based pyramid, you can use the formula:

\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

1. **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:

\[
A = 8 \times 8 = 64 \text{ cm}^2
\]

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:

\[
V = \frac{1}{3} \times 512 \text{ cm}^3 = \frac{512}{3} \text{ cm}^3 \approx 170.67 \text{ cm}^3
\]

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!