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

Answer:

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

Step-by-step explanation:

The volume of a pyramid is

$V = \dfrac{1}{3} \times B\times H$

where the height of the pyramid is 5

$V = \dfrac{1}{3} \times B\times 5$

$V = \dfrac{5}{3} B \ units ^3$

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:

$\dfrac{V_p}{V_c}= \dfrac{\dfrac{5}{3}B}{3B}$

$\dfrac{V_p}{V_c}= \dfrac{5}{9}$

$9 V_p = 5 V_c$

$V_c = 1.8 \ V_p$

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