A right rectangular pyramid has an altitude of 35 m, a length of 26 m, and a width of 31 m. What is the volume of the pyramid in m ^ 3 (1 point)
O 84, 630m ^ 3
O 30.67m ^ 3
O 9, 403.33m ^ 3
O 28, 210m ^ 3
1 720 cm
2 9,403.33 m
3 296,874.67ft
4 880 cm
5 37,500 ft
To find the volume of a right rectangular pyramid, you can use the formula:
Volume = (1/3) × base area × height
The base area of a rectangle is calculated by multiplying the length and width. In this case, the length is 26 m and the width is 31 m, so the base area is:
Base area = 26 m × 31 m = 806 m^2
Now, plug the values into the formula:
Volume = (1/3) × 806 m^2 × 35 m
Volume = 9403.33 m^3
Therefore, the volume of the pyramid is 9,403.33 m^3. The correct option is O 9,403.33m^3.
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)
890, 624ft .^ 3
2,671, 872ft .^ 3
98.33ft .^ 3
296.874 * 0.67ft .^ 3
To find the volume of a pyramid, you can use the formula:
Volume = (1/3) × base area × height
First, calculate the base area of the pyramid. Since the base is a square with sides of 112 feet, the base area is:
Base area = 112 ft × 112 ft = 12,544 ft^2
Now, plug the values into the formula:
Volume = (1/3) × 12,544 ft^2 × 71 ft
Volume = 298,624 ft^3
Therefore, the volume of the pyramid at the Louvre Museum is 298,624 ft^3. The correct option is 298,624ft^3.
J Juice brand wants to create a new bottle for their products. Their marketing department wants to design a pyramid- shaped bottle with a base that is 8 cm by 15 cm, and has an altitude of 22 cm. How much juice will this new bottle hold? (1 point)
O 7, 920c * m ^ 3
2.64c * m ^ 3
O 880c * m ^ 3
15c * m ^ 3
To find the volume of the pyramid-shaped bottle, you can use the formula:
Volume = (1/3) × base area × height
The base area of a rectangle is calculated by multiplying the length and width. In this case, the length is 15 cm and the width is 8 cm, so the base area is:
Base area = 15 cm × 8 cm = 120 cm^2
Now, plug the values into the formula:
Volume = (1/3) × 120 cm^2 × 22 cm
Volume = 880 cm^3
Therefore, the new pyramid-shaped bottle will hold 880 cm^3 of juice.
The correct option is O 880 cm^3.
A construction company is digging a drainage trench. It makes the shape of an upside-down rectangular pyramid. The top opening will be 30 ft. wide by 250 ft. long, and the deepest part in the middle will be 15 ft. What is the capacity for this trench? (1 point)
O 37,500 ft.3
O 98.33 ft.3
O337,500 ft.3
O 112, 500ft .^ 3
To find the capacity of the trench, we need to find the volume of the upside-down rectangular pyramid. The formula to find the volume of a rectangular pyramid is:
Volume = (1/3) × base area × height
First, we need to find the base area. The top opening is given as 30 ft. wide by 250 ft. long, so the base area is:
Base area = 30 ft × 250 ft = 7500 ft^2
Next, we have to find the height of the pyramid. The deepest part in the middle is given as 15 ft.
Now, we can plug the values into the volume formula:
Volume = (1/3) × 7500 ft^2 × 15 ft
Volume = 112,500 ft^3
Therefore, the capacity of the trench is 112,500 ft^3. The correct option is O 112,500 ft^3.
I apologize for any confusion caused by my previous responses. Let's go through the calculations again.
1. The volume of the pyramid at the Louvre Museum is:
Volume = (1/3) × base area × height
The base area is 112 ft × 112 ft = 12,544 ft^2.
The height is 71 ft.
Volume = (1/3) × 12,544 ft^2 × 71 ft = 296,874.67 ft^3
2. The volume of the pyramid-shaped bottle for J Juice brand is:
Volume = (1/3) × base area × height
The base area is 8 cm × 15 cm = 120 cm^2.
The height is 22 cm.
Volume = (1/3) × 120 cm^2 × 22 cm = 880 cm^3
3. The volume of the upside-down rectangular pyramid for the drainage trench is:
Volume = (1/3) × base area × height
The base area is 30 ft × 250 ft = 7500 ft^2.
The height is 15 ft.
Volume = (1/3) × 7500 ft^2 × 15 ft = 37,500 ft^3
Therefore, the correct options are:
1. 296,874.67 ft^3
2. 880 cm^3
3. 37,500 ft^3
To find the volume of a right rectangular pyramid, you can use the formula: Volume = (1/3) * base area * height.
In this case, the base of the pyramid is a rectangle with length 26 m and width 31 m, so the base area is 26 * 31 = 806 m^2.
Given that the altitude (height) of the pyramid is 35 m, you can now calculate the volume as follows:
Volume = (1/3) * 806 m^2 * 35 m
Simplifying the equation:
Volume = (1/3) * 806 m^2 * 35 m
= (806 * 35) / 3
= 28210 m^3
Therefore, the volume of the pyramid is 28,210 m^3.
So the correct answer is O 28,210m^3.