Thomas sketches this square-based pyramid. Each edge of the base measures 8 centimeters, as shown in the image. What is the volume of Thomas' pyramid, rounded to the nearest whole cubic centimeter?

1 answer

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

\[ V = \frac{1}{3} \times B \times h \]

where \( B \) is the area of the base and \( h \) is the height of the pyramid.

Step 1: Calculate the area of the base

Since the base is a square with each side measuring 8 centimeters, the area \( B \) is given by:

\[ B = \text{side}^2 = 8 , \text{cm} \times 8 , \text{cm} = 64 , \text{cm}^2 \]

Step 2: Determine the height

Next, we need to find the height \( h \) of the pyramid. However, since the height is not provided in the prompt, we cannot calculate the volume without it. If we assume the height is given, we will denote the height as \( h \).

Step 3: Substitute into the volume formula

Now substituting the area of the base into the volume formula gives us:

\[ V = \frac{1}{3} \times 64 , \text{cm}^2 \times h \]

This simplifies to:

\[ V = \frac{64h}{3} , \text{cm}^3 \]

Conclusion

To find the exact volume, we need the height \( h \). Please provide the height of the pyramid, or if it was given or can be inferred, let me know so I can proceed with the final calculation of the volume rounded to the nearest whole cubic centimeter.