Answer:
Part 1) The volume of the prism is 3 times greater than the volume of the pyramid
Part 2) The prism would fill only one-third
Part 3) The cylinder and the cone
Step-by-step explanation:
Part 1) How do their volumes compare?
we know that
The volume of a rectangular prism is equal to
[tex]Vprism=BH[/tex]
where
B is the area of the base of rectangular prism
H is the height of the prism
The volume of a rectangular pyramid is equal to
[tex]Vpyramid=\frac{1}{3}BH[/tex]
where
B is the area of the base of rectangular pyramid
H is the height of the pyramid
Compare the volumes
[tex]Vprism=BH[/tex] -----> equation A
[tex]Vpyramid=\frac{1}{3}BH[/tex] -----> equation B
substitute equation A in equation B
[tex]Vpyramid=\frac{1}{3}Vprism[/tex]
[tex]Vprism=(3)Vpyramid[/tex]
The volume of the prism is 3 times greater than the volume of the pyramid
Part 2) If the pyramid was full of water, how much of the prism would it fill up?
Remember that
[tex]Vpyramid=\frac{1}{3}Vprism[/tex]
therefore
The prism would fill only one-third
Part 3) Name another pair of three-dimensional objects that have a relationship similar to this
we have the cylinder and the cone
The volume of the cylinder is equal to
[tex]Vcylinder=\pi r^{2}h[/tex]
The volume of the cone is equal to
[tex]Vcone=\frac{1}{3}\pi r^{2}h[/tex]
Compare the volumes
[tex]Vcylinder=(3)Vcone[/tex]
The volume of the cylinder is 3 times greater than the volume of the cone
This true statement is that the volume of the pyramid is greater than the volume of the prism.
The relationship between the volumes of a rectangular pyramid and a rectangular prism that have the same base and same height is:
[tex]V_1 = \frac 13 V_2[/tex]
Where:
V1 represents the volume of the pyramid, and V2 represents the volume of the prism.
This means that, the volume of the pyramid is greater than the volume of the prism.
And also, if the pyramid was full of water, 1/3 of it would fill the prism
A pair of three-dimensional objects that have a relationship similar to this is the cone and the cylinder
Read more about three-dimensional objects at:
https://brainly.com/question/1972490
