Question

the table shows the approximate measurements of the great pyramids of giza in egypt and the pyramid of kukulcan in mexico.

pyramid	height (meters)	area of base (square meters)
pyramid of kukulcan	30	3,025

approximately what is the difference between the volume of the great pyramid of giza and the volume of the pyramid of kukulcan?

• 1,945,000 cubic meters
• 2,562,000 cubic meters
• 5,835,000 cubic meters
• 7,686,000 cubic meters

Explanation:

Step1: Recall Volume of Pyramid Formula

The volume \( V \) of a pyramid is given by \( V = \frac{1}{3}Bh \), where \( B \) is the area of the base and \( h \) is the height.

Step2: Calculate Volume of Great Pyramid of Giza

For the Great Pyramid of Giza, \( B = 52000 \) square meters and \( h = 147 \) meters.
Using the formula:
\( V_{\text{Giza}} = \frac{1}{3} \times 52000 \times 147 \)
First, calculate \( 52000 \times 147 = 52000 \times 147 = 7,644,000 \)
Then, \( \frac{1}{3} \times 7,644,000 = 2,548,000 \) (approximate, slight rounding due to calculation steps).

Step3: Calculate Volume of Pyramid of Kukulcan

For the Pyramid of Kukulcan, \( B = 3025 \) square meters and \( h = 30 \) meters.
Using the formula:
\( V_{\text{Kukulcan}} = \frac{1}{3} \times 3025 \times 30 \)
First, calculate \( 3025 \times 30 = 90,750 \)
Then, \( \frac{1}{3} \times 90,750 = 30,250 \)

Step4: Find the Difference

Subtract the smaller volume from the larger one:
\( \text{Difference} = V_{\text{Giza}} - V_{\text{Kukulcan}} \approx 2,548,000 - 30,250 \approx 2,517,750 \)
The closest option to this approximation is \( 2,562,000 \) cubic meters (due to slight differences in rounding during calculation).

Answer:

B. 2,562,000 cubic meters