A cylinder has a height of 4 inches greater than the radius of its base. Find the radius and the height to the nearest inch if the volume of the cylinder is 5pi cubic inches.
Accepted Solution
A:
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]