Use the formula for the volume of a rectangular pyramid to find the volume of a pyramid-shaped tent whose height is 75 in., width is 111 in., and length is 111 in. when standing.
The formula for the volume of a rectangular pyramid is:
V = (1/3) * base area * height
To use this formula, we need to find the base area of the pyramid. Since the tent is rectangular, its base area is simply the length times the width:
base area = length * width
base area = 111 in. * 111 in.
base area = 12,321 in.^2
Now we can plug in the values we have:
V = (1/3) * base area * height
V = (1/3) * 12,321 in.^2 * 75 in.
V = 308,025 in.^3
Therefore, the volume of the pyramid-shaped tent is 308,025 cubic inches.
A cell phone telecommunication tower stands in the shape of a rectangular pyramid. The tower stands 80 m tall and rests on a base that is 15 m by 20 m. What is the volume of the tower?
The formula for the volume of a rectangular pyramid is:
V = (1/3) * base area * height
To use this formula, we need to find the base area of the pyramid. The base of the tower is a rectangle with dimensions of 15 m by 20 m, so the base area is:
base area = length * width
base area = 15 m * 20 m
base area = 300 m^2
Now we can plug in the values we have:
V = (1/3) * base area * height
V = (1/3) * 300 m^2 * 80 m
V = 8,000 m^3
Therefore, the volume of the tower is 8,000 cubic meters.
A holiday ornament in the shape of a square pyramid has the following dimensions: 2.75 x 2.75 x 2.75 in. What is the approximate volume of the ornament? Round your answer to the nearest hundredth.
The formula for the volume of a square pyramid is:
V = (1/3) * base area * height
To use this formula, we need to find the base area of the pyramid. Since the ornament is a square pyramid, the base is a square with sides of 2.75 in, so the base area is:
base area = side length^2
base area = (2.75 in)^2
base area = 7.5625 in^2
Now we can plug in the values we have:
V = (1/3) * base area * height
V = (1/3) * 7.5625 in^2 * 2.75 in
V = 6.5404 in^3
Rounding this to the nearest hundredth, we get:
V ≈ 6.54 in^3
Therefore, the approximate volume of the ornament is 6.54 cubic inches.
The formula for the volume of a rectangular pyramid is given by V = (1/3) * l * w * h, where V is the volume, l is the length, w is the width, and h is the height of the pyramid.
Given:
Height (h) = 75 in.
Width (w) = 111 in.
Length (l) = 111 in.
Using the formula:
V = (1/3) * l * w * h
Substituting the given values:
V = (1/3) * 111 * 111 * 75
Evaluating the expression:
V = (1/3) * 111 * 111 * 75
V = (1/3) * 10964175
V ≈ 3654725
Therefore, the volume of the pyramid-shaped tent is approximately 3,654,725 cubic inches.
To find the volume of a rectangular pyramid, you can use the formula:
Volume = (1/3) * base area * height
In this case, we need to find the base area first. Since the tent is rectangular, the base area will be the area of a rectangle, which is calculated by multiplying the length and width:
Base area = length * width
Given that the length is 111 in. and the width is also 111 in., we can calculate the base area:
Base area = 111 in. * 111 in.
Base area = 12321 in²
Now, we can substitute the values into the volume formula to find the volume:
Volume = (1/3) * 12321 in² * 75 in.
Volume = 136900 in³
Therefore, the volume of the pyramid-shaped tent when standing is 136900 cubic inches.