Respuesta :
Answer:
[tex]h=5in, r=1in[/tex]
Step-by-step explanation:
The volume of a cylinder is:
[tex]V=\pi*r^2*h[/tex]
where [tex]r[/tex] is the radius and [tex]h[/tex] is the height.
The height is 4 inches greater that the radius, so:
[tex]h=r+4in[/tex]
Substituting this in the formula for volume:
[tex]V=\pi*r^2*(r+4)[/tex]
the volume is [tex]V=5\pi in^3[/tex]
thus:
[tex]5\pi in^3=\pi*r^2*(r+4in)[/tex]
Dividing everything between pi:
[tex]5in^3=r^2*(r+4in)[/tex]
[tex]5in^3=r^3*+4r^2[/tex]
We can see that the solution for this is [tex]r=1in[/tex]
since [tex](1)^3*+4(1)^2=1+4=5[/tex]
We have the radius, now we find the height:
[tex]h=r+4in=1in + 4in = 5in[/tex]
[tex]h=5in, r=1in[/tex]
