A climbing pyramid in a children’s playground has a volume of 440/3 m3 . The base is a rectangle, measuring 8 m by 11 m. What is the height of the pyramid?(1 point) m
To find the height of the pyramid, you can use the formula for the volume of a pyramid:
Volume = (1/3) * base * height
Given that the volume is 440/3 m^3 and the base is a rectangle measuring 8 m by 11 m, you can plug these values into the formula and solve for the height:
440/3 = (1/3) * 8 * 11 * height
440 = 88 * height
height = 440 / 88
height = 5
Therefore, the height of the pyramid is 5 meters.
A rectangular prism has a volume of 27 in.3 . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?(1 point) in.3
The volume of a rectangular prism is given by the formula:
Volume = length * width * height
Given that the volume of the prism is 27 in^3 and the dimensions are congruent (meaning the length, width, and height are the same), you can represent the dimensions of the prism as x, x, x.
So, the volume of the prism can be expressed as:
27 = x * x * x
27 = x^3
To find the value of x (which will be the dimensions of the rectangular pyramid), you can cube root both sides:
x = ∛27
x = 3
Now that you know the dimensions of the rectangular pyramid (3 inches by 3 inches by 3 inches), you can calculate the volume of the pyramid using the formula for the volume of a pyramid:
Volume_pyramid = (1/3) * base * height
Plugging in the values:
Volume_pyramid = (1/3) * 3 * 3 * 3
Volume_pyramid = 9 in^3
Therefore, the volume of the pyramid is 9 in^3.
Which shape has the larger volume? How much larger is it? (1 point) Responses The pyramid has a larger volume by three times. The pyramid has a larger volume by three times. The volumes are the same. The volumes are the same. The prism has a larger volume by 13 times. The prism has a larger volume by Start Fraction 1 over 3 End Fraction times. The prism has a larger volume by three times.
The pyramid and prism in the given scenario have volumes of 9 in^3 and 27 in^3, respectively.
Therefore, the prism has a larger volume than the pyramid by 13 times.
A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 600 ft.3 , what is the volume of the pyramid? (1 point) Responses 200 ft.3 200 ft. cubed 600 ft.3 600 ft. cubed 400 ft.3 400 ft. cubed 1,800 ft.3
Since both shapes have the same height and a triangular base, the volume of a prism and a pyramid with the same base area will have a ratio of 1:1.
Given that the volume of the prism is 600 ft^3, the volume of the pyramid will also be 600 ft^3.
Therefore, the volume of the pyramid is 600 ft^3.