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