Question

According to Cavalieri’s Principle, if a cone and a pyramid have the same height, which of the following answer choices is true?

Question 12 options:

A)They have equal volumes.


B)They have equal surface areas.


C)They have equal volumes if their bases have equal areas.


D)They have equal surface areas if their bases have equal areas.

Answer 1

C

Explanation:

Answer 2

Option (C).

Explanation:

If a cone and a pyramid have same height,

Volume of a cone =
`(1)/(3)(\text{Area of the base})* (\text{height}))`

=
`(1)/(3)(A_(1))* (h)`

Volume of a pyramid =
`(1)/(3)(\text{Area of the base})* (\text{height})`

=
`(1)/(3)(A_(2))(h)`

As we can see if area of the bases of cone and pyramid are same, their volumes will be same.

Cavalier's Principle states, two solids having same heights and all cross sections of equal areas at the equal distances from the base, will have the same volumes.

Therefore, as per Cavalier's Principle, option (C) will be the answer.