Answer :
Answer:
The domain of V(h(r)) is restricted to values of r greater than 0
V(h(r)) = 3.5πr^3
The volume depends on the radius of the cylinder
Step-by-step explanation:
Edgenuity
Volume of a cylindrical silo is given by,
[tex]V=\pi r^{2}h[/tex]
Here, [tex]V=[/tex] Volume of the silo
[tex]r=[/tex] Radius of the cylindrical silo
[tex]h=[/tex] Hight of the silo
And height of the silo is defined by the function,
[tex]h(r)=3.5r[/tex]
Option (1)
To get the volume of [tex]100[/tex] cubic feet, radius must be [tex]2[/tex] feet.
Height of the silo can be derived from the function,
[tex]h(2)=3.5(2)[/tex]
[tex]=7[/tex] feet
Therefore, volume of the silo = [tex]\pi r^{2} h[/tex]
= [tex]\pi (2)^2(7)[/tex]
= [tex]28\pi[/tex]
= [tex]87.96[/tex] feet³
Since, [tex]87.96<100[/tex] cubic feet
Statement is false.
Option (2)
Since, [tex]V=\pi r^{2} h[/tex]
And [tex]h(r)=3.5r[/tex]
Therefore, [tex]V[h(r)]=\pi r^{2}(3.5r)[/tex]
[tex]V[h(r)]=3.5\pi r^{3}[/tex]
Domain of the function 'V' will be [tex]r>0[/tex].
Statement is true.
Option (3)
Output of V is the input of h.
From the function,
[tex]V[h(r)]=3.5\pi r^{3}[/tex]
Volume (output value) of the silo depends on the output value of [tex]h(r)[/tex].
Therefore, statement is false.
Option (4)
[tex]V[h(r)]=3.5\pi r^{3}[/tex]
Volume depends on the radius of the cylinder.
Since, output value of the volume depends on the radius.
Statement is true.
Options (2) and (4) are true.
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