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

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

890,624 ft.3
890,624 feet cubed

98.33 ft.3

Answer 1

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

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

In this case, the base of the pyramid is a square with each side measuring 112 feet, and the height (altitude) is 71 feet.

Step 1: Calculate the Base Area

The area of the base (which is a square) can be calculated as:

\[ \text{Base Area} = \text{side} \times \text{side} = 112 , \text{feet} \times 112 , \text{feet} = 12,544 , \text{ft}^2 \]

Step 2: Calculate the Volume

Now, substitute the base area and height into the volume formula:

\[ \text{Volume} = \frac{1}{3} \times 12,544 , \text{ft}^2 \times 71 , \text{feet} \]

Calculating that:

\[ \text{Volume} = \frac{1}{3} \times 12,544 \times 71 = \frac{890,624}{3} , \text{ft}^3 \approx 296,874.67 , \text{ft}^3 \]

Thus, the volume of the pyramid at the Louvre Museum is approximately 296,874.67 ft³.

So the correct response is:

296,874.67 ft³.