Answer:
[tex]\large\boxed{H=\dfrac{6}{\sqrt[3]{\pi}}}[/tex]
Step-by-step explanation:
The formula of a volume of a cylinder:
[tex]V=\pi r^2H[/tex]
r - radius
H - height
We have V = 24 and H = 3r.
Substitute:
[tex]24=\pi r^2(3r)\\\\24=3\pi r^3\qquad\text{divide both sides by}\ 3\pi\\\\\dfrac{24}{3\pi}=r^3\\\\r^3=\dfrac{8}{\pi}\to r=\sqrt[3]{\dfrac{8}{\pi}}\\\\r=\dfrac{\sqrt[3]{8}}{\sqrt[3]{\pi}}\\\\r=\dfrac{2}{\sqrt[3]{\pi}}\\\\H=3r\to H=3\cdot\dfrac{2}{\sqrt[3]{\pi}}\to H=\dfrac{6}{\sqrt[3]{\pi}}[/tex]
