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
[tex]V = \dfrac{1}{3} \times B\times H[/tex]
where the height of the pyramid is 5
[tex]V = \dfrac{1}{3} \times B\times 5[/tex]
[tex]V = \dfrac{5}{3} B \ units ^3[/tex]
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:
[tex]\dfrac{V_p}{V_c}= \dfrac{\dfrac{5}{3}B}{3B}[/tex]
[tex]\dfrac{V_p}{V_c}= \dfrac{5}{9}[/tex]
[tex]9 V_p = 5 V_c[/tex]
[tex]V_c = 1.8 \ V_p[/tex]
Hence, the volume of the right cylinder is 1.8 times the volume of the pyramid
