Volume of Pyramids Quick Check

Question

3 of 53 of 5 Items
Question
Use the volume formula to determine the volume of the pyramid at the Louvre Museum if it has a base that is 112 feet long on each side and has an altitude of 71 feet.(1 point)
Responses

296,874.67 ft.3
296,874.67 feet cubed

98.33 ft.3
98.33 feet cubed

890,624 ft.3
890,624 feet cubed

2,671,872 ft.3
2,671,872 feet cubed

Answer 1

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

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

where \( V \) is the volume, \( B \) is the area of the base, and \( h \) is the height (altitude) of the pyramid.

1. Calculate the area of the base (B): The base is a square, with each side measuring 112 feet. Thus, the area \( B \) is: \[ B = \text{side}^2 = 112 , \text{ft} \times 112 , \text{ft} = 12,544 , \text{ft}^2 \]

2. Use the altitude (h): The altitude \( h \) of the pyramid is given as 71 feet.

3. Substitute the values into the volume formula: \[ V = \frac{1}{3} \times 12,544 , \text{ft}^2 \times 71 , \text{ft} \]

4. Calculate the volume: \[ V = \frac{1}{3} \times 12,544 \times 71 \approx \frac{1}{3} \times 891,584 \approx 297,194.67 , \text{ft}^3 \]

The closest response option to our calculated volume is:

296,874.67 ft³