Answer:
[tex]\large\boxed{height=\dfrac{3}{4}y}[/tex]
Step-by-step explanation:
The formulas of a volume of
a cylinder:
[tex]V_1=\pi r^2h[/tex]
a cone:
[tex]V_2=\dfrac{1}{3}\pi r^2h[/tex]
r - radius
h - height
Substitute
The cylinder:
[tex]V_1=\pi x^2y[/tex]
The cone:
[tex]V_2=\dfrac{1}{3}\pi (2x)^2h=\dfrac{1}{3}\pi(4x^2)h=\dfrac{4}{3}\pi x^2h[/tex]
The cylinder and the cone have the same volume. Therefore we have the equation:
[tex]\dfrac{4}{3}\pi x^2h=\pi x^2y[/tex] divide both sides by πx²
[tex]\dfrac{4}{3}h=y[/tex] multiply both sides by 3/4
[tex]\dfrac{3\!\!\!\!\diagup^1}{4\!\!\!\!\diagup_1}\cdot\dfrac{4\!\!\!\!\diagup^1}{3\!\!\!\!\diagup_1}h=\dfrac{3}{4}y\\\\h=\dfrac{3}{4}y[/tex]
