A prism and pyramid bothe have this triangluar base=20Ft. If both shapes have the same hight and the volume of the prism is 600ft^3, what is the volume of the pyramid.

Answer 1

To find the volume of the pyramid, we first need to calculate the area of the triangular base.

Area of a triangle = 1/2 * base * height

In this case, the base is 20 ft and the height of the triangle is the height of the prism (since both shapes have the same height). Let's call the height of the prism (and the pyramid) "h".

So, the area of the triangular base = 1/2 * 20 * h = 10h

Now, we know the volume of the prism is 600 ft^3. The volume of a prism is given by:

Volume of a prism = area of base * height

Substitute the values we have:

600 = 10h * h
600 = 10h^2

Solving for h:

h^2 = 60
h = √60
h ≈ 7.75 ft

Now that we have the height of the pyramid, we can calculate its volume using the formula for the volume of a pyramid:

Volume of a pyramid = 1/3 * area of base * height

Substitute the values we have:

Volume of the pyramid = 1/3 * 10 * 7.75 ≈ 25.83 ft^3

Therefore, the volume of the pyramid is approximately 25.83 ft^3.