According to Cavalieri’s Principle, which pair of shapes would have equal volumes?

Question 5 options:

a)

a cylinder and a sphere with the same radius

b)

a cone and a cylinder with equal base areas and heights

c)

a cylinder and a right rectangular prism with equal heights

d)

a cone and a pyramid with equal base areas and heights

Cavalieri's principle tells us about the volume of two shapes. The correct option is a cylinder and a right rectangular prism with equal heights.

What is Cavalieri's principle?

According to Cavalieri's principle if two objects have the same height and same base area throughout their heights, then the volume of both objects would be the same.

As we know according to Cavalieri’s Principle, the object should have the same height. Also, the area of the object should be the same throughout the height, but since in a cone the area is gradually decreasing towards the top, and the area of the sphere is also decreasing about the top and the bottom of the sphere. therefore, the options with the object such as cone and sphere are not the correct options.

Thus, the correct option is a cylinder and a right rectangular prism with equal heights as shown in the below image.

Learn more about Cavalieri's principle:

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