The volume of a shape is the amount of space in the shape
The radius of the cylinder is 3 mm
The given parameters of the cone are:
Radius = 3mm
Height = 6mm
The volume of the cone is:
[tex]V =\frac 13\pi r^2h[/tex]
So, we have:
[tex]V =\frac 13\pi * 3^2 * 6[/tex]
The volume of a cylinder is:
[tex]V= \pi r^2h[/tex]
The height is:
Height = 2 mm
So, we have:
[tex]V= \pi r^2 * 2[/tex]
The volumes are equal.
So, we have:
[tex]\pi r^2 * 2 = \frac 13\pi * 3^2 * 6[/tex]
Divide the common factors
[tex]r^2 = \frac 13 * 3^2 * 3[/tex]
Evaluate the products
[tex]r^2 = 9[/tex]
Take the square roots of both sides
[tex]r = 3[/tex]
Hence, the radius of the cylinder is 3 mm
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