If a triangular prism and a cylinder have the same height and the same volume, what must be true about their bases?
The triangular prism has a larger base than the cylinder.
Their bases have the same area.
The cylinder has a larger base than the triangular prism.
Their bases are the same shape.
since the volume is Bh, if the height h is the same, so must be the area B of the bases.
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What is the shape of the bases of cylinder and rectangular
Answer (Their bases are the same)
To understand why their bases must have the same area, let's start by finding the formulas for finding the volume of both the triangular prism and the cylinder.
The volume of a triangular prism can be found by multiplying the area of the base by the height. So, the formula is:
Volume of triangular prism = (Area of base) * (Height)
On the other hand, the volume of a cylinder is found by multiplying the area of the base by the height. So, the formula is:
Volume of cylinder = (Area of base) * (Height)
Given that the height is the same for both the prism and the cylinder, we can set their volumes equal to each other:
(Area of base for prism) * (Height) = (Area of base for cylinder) * (Height)
As you can see, the height cancels out on both sides of the equation. This leaves us with:
Area of base for prism = Area of base for cylinder
Therefore, the only necessary condition for the triangular prism and the cylinder to have the same volume and height is that their bases must have the same area. So, the correct answer is "Their bases have the same area."