Answer :
First, you must find the original volume of the prism by applying the following formula:
V1=HxB
V1 is the original volume of the prism.
H is the height of the prism (H=10 ft).
B is the base are of the prism (B=5 ft2)
So, the original volume is:
V1=HxB
V1=(10 ft)(5 ft2)
V1=50 ft2
When the prism is dilated by a factor of 6/5, its volume is:
V2=(V1)*(6/5)^3
V2=(50 ft³)*(6/5)^3
V2= 86.4 ft³
What is the volume of the dilated prism?
The answer is: 86.4 ft³
V1=HxB
V1 is the original volume of the prism.
H is the height of the prism (H=10 ft).
B is the base are of the prism (B=5 ft2)
So, the original volume is:
V1=HxB
V1=(10 ft)(5 ft2)
V1=50 ft2
When the prism is dilated by a factor of 6/5, its volume is:
V2=(V1)*(6/5)^3
V2=(50 ft³)*(6/5)^3
V2= 86.4 ft³
What is the volume of the dilated prism?
The answer is: 86.4 ft³
Step [tex]1[/tex]
Find the volume of the original prism
we know that
the volume of the prism is equal to
[tex]V=Bh[/tex]
where
B is the area of the base of the prism
h is the height of the prism
in this problem we have
[tex]B=5\ ft^{2}\\h=10\ ft[/tex]
substitute in the formula of volume
[tex]V=5*10=50\ ft^{3}[/tex]
Step [tex]2[/tex]
Find the volume of the dilated prism
we know that
[tex]volume\ of\ the\ dilated\ prism=[scale\ factor^{3}]*volume\ of\ the\ original\ prism[/tex]
we have
[tex]scale\ factor=\frac{6}{5}[/tex]
[tex]volume\ of\ the\ original\ prism=50\ ft^{3}[/tex]
substitute the values
[tex]volume\ of\ the\ dilated\ prism=(\frac{6}{5})^{3}*50[/tex]
[tex]volume\ of\ the\ dilated\ prism=1.728*50\\ \\volume\ of\ the\ dilated\ prism=86.4\ ft^{3}[/tex]
therefore
the answer is
the volume of the dilated prism is [tex]86.4\ ft^{3}[/tex]