Question

The cross-sectional areas of a right pyramid and a right cylinder are congruent. The pyramid has a height of five units, and a right triangle has a height of three units. Which conclusion could be made from the given information

Answer 1

the volume of the right cylinder is 1.8 times the volume of the pyramid

Explanation:

The volume of a pyramid is

`V = (1)/(3) * B* H`

where the height of the pyramid is 5

`V = (1)/(3) * B* 5`

`V = (5)/(3) B \ units ^3`

On the other hand, the volume of a right cylinder is

V = BH

where the height of the right cylinder = 3 units

V = 3 B units³

Since we know that the cross-sectional areas are congruent, comparing the two-volume, we have the ratio of their volumes to be:

`(V_p)/(V_c)= ((5)/(3)B)/(3B)`

`(V_p)/(V_c)= (5)/(9)`

`9 V_p = 5 V_c`

`V_c = 1.8 \ V_p`

Hence, the volume of the right cylinder is 1.8 times the volume of the pyramid