Answer:
Part a) The volume of the prism Q is two times the volume of the prism P
Part b) The volume of the prism Q is two times the volume of the prism P
Step-by-step explanation:
Part 18) we know that
The volume of a rectangular prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base
h is the height of the prism
a) Suppose the bases of the prisms have the same area, but the height of prism Q is twice the height of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=B(2h)=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
so
The volume of the prism Q is two times the volume of the prism P
b) Suppose the area of the base of prism Q is twice the area of the base of prism P. How do the volumes compare?
Volume of prism Q
[tex]VQ=(2B)h=2(Bh)[/tex]
Volume of prism P
[tex]VP=Bh[/tex]
Compare
[tex]VQ=2VP[/tex]
The volume of the prism Q is two times the volume of the prism P
