A prism and a Pyramid both have this triangular base. If both shapes have the same height and the volume of the Pyramid is 210 cubic units., what is the volume of the prism. The height is 5 in
if the prism and the pyramid have the same base and height, the pyramid has 1/3 the volume of the prism: in this case, 210/3 = 70.
The actual height does not matter.
Thank you for the correction. You are correct that if the pyramid and prism have the same base and height, the volume of the pyramid will be 1/3 the volume of the prism. In this case, the volume of the prism would be 3 times the volume of the pyramid, or 3*210 = 630 cubic units.
To solve this problem, we need to first find the area of the triangular base, which will be the same for both the prism and the pyramid.
The formula for the area of a triangle is: Area = (base * height) / 2
Let's assume the base of the triangle is denoted by 'b'. The area of the triangular base for both the prism and the pyramid will be (b * 5) / 2.
Since the height is the same for both shapes, the only difference in their volumes will be the base areas.
Now, we know the volume of the pyramid is 210 cubic units, and the formula for the volume of a pyramid is: Volume = (base area * height) / 3
Plugging in the values we have, we can rearrange the formula to solve for the base area:
210 = [(b * 5) / 2 * 5] / 3
To solve for the base area, we isolate 'b':
210 * 3 = (b * 5) / 2 * 5
630 = (b * 5) / 2
To find 'b', we multiply both sides by 2 and divide by 5:
(630 * 2) / 5 = b
252 = b
So, the base of the triangular shape has an area of 252 square units.
Now, we can find the volume of the prism using the same formula:
Volume = (base area * height)
Volume = 252 * 5
Volume = 1260 cubic units
Therefore, the volume of the prism is 1260 cubic units.