Answer:
Height(h) of the cylinder is: [tex]h=9cm[/tex]
Step-by-step explanation:
Height(H) of cone = 12 cm
Radius(R) of the cone =12 cm
Radius(r) of the cylinder=8 cm
Height(h) of the cylinder=?
Volume of the cone=Volume of the cylinder
[tex]\pi *R^2*\frac{H}{3} =\pi *r^2*h[/tex]
Dividing by '[tex]\pi[/tex]' both sides:
[tex]R^2*\frac{H}{3}=r^2*h[/tex]
Putting the values in the formula:
[tex]12^2*\frac{12}{3}= 8^2*h[/tex]
[tex]144*4=64*h\\\\576=64*h\\\\[/tex]
Dividing by '64' both sides:
[tex]h=576/64[/tex]
[tex]h=9cm[/tex]
The height(h) of the cylinder is : [tex]h=9cm[/tex]
