A prisim and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prisim is 600ft 3 what is the volume of the pyramid
To find the volume of the pyramid, we can use the formula for the volume of a prism and pyramid, which is given by:
Volume of prism = base area of prism x height
Volume of pyramid = 1/3 x base area of pyramid x height
Since the prism and pyramid have the same height and base, the only difference is the factor of 1/3 in the volume formula.
Given that the volume of the prism is 600 ft^3, we can find the base area of the prism by dividing the volume by the height:
Base area of prism = Volume of prism / height
Base area of prism = 600 ft^3 / height
We know that the volume of the pyramid is 1/3 times the volume of the prism:
Volume of pyramid = 1/3 x Volume of prism
Volume of pyramid = 1/3 x 600 ft^3
Volume of pyramid = 200 ft^3
Therefore, the volume of the pyramid is 200 ft^3.
The base is 20
Given that the base of both the prism and the pyramid is a triangle with a base of 20 units, let's calculate the area of this base first:
Area of a triangle = (base x height) / 2
Area of base = (20 x height) / 2
Since the height is the same for both the prism and the pyramid, we can find the area of the base:
Area of base = (20 x height) / 2
Next, we know that the volume of the prism is 600 ft^3:
Volume of prism = base area of prism x height
Volume of prism = 600 ft^3
Since the height is the same for both shapes, we can substitute the area of the base into the volume formula:
600 = (20 x height) / 2 x height
600 = 10 x height^2
height^2 = 60
height = √60 ≈ 7.75 ft
Now that we have found the height, we can calculate the volume of the pyramid using the formula:
Volume of pyramid = 1/3 x base area of pyramid x height
Volume of pyramid = 1/3 x (20 x 7.75) / 2 x 7.75
Volume of pyramid = 1/3 x 77.5
Volume of pyramid ≈ 25.83 ft^3
Therefore, the volume of the pyramid is approximately 25.83 ft^3.