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

Answer 1

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.

Answer 2

The base is 20

Answer 3

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.