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A rectangular prism and a cylinder have the same height. The length of each side of the prism base is equal to the diameter of the cylinder. Which shape has a greater volume? Drag and drop the labels to explain your answer.

1 Answer

5 votes

Answer:

The rectangular prism has the greater volume

Explanation:

Given

Prism:


Length = Width = a


Height = h

Cylinder


Diameter = a


Height = h

Required

Shape with greater volume

The volume of a rectangular prism is:


Volume = Length * Base * Height

So, we have:


V_1 = a*a*h


V_1 = a^2h

The volume of a cylinder is:


Volume = \pi r^2h

Where


r = (d)/(2)


r = (a)/(2)

So, we have:


V_2 = \pi *(a/2)^2 h


V_2 = \pi *(a^2)/(4) h


\pi = 3.14

So:


V_2 = 3.14*(a^2)/(4) h


V_2 = (3.14)/(4) a^2h


V_2 = 0.785 a^2h

So, we have:


V_1 = a^2h


V_2 = 0.785 a^2h

Both expressions have the same factor but different coefficient

The expression with greater coefficient has the greater volume

So, the
rectangular
prism \\ has the
greater
volume

Because:
1 > 0.785

User Curtis Xiao
by
7.9k points

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