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A foam cylinder, with a diameter of 3 inches and height of 6 inches, is carved into the shape of a cone. What is the maximum volume of a cone that can be carved? Round your answer to the hundredths place.

Respuesta :

The formula for the volume (V) of the cone is

[tex]V=\frac{1}{3}\pi r^2h[/tex]

Given

[tex]\begin{gathered} r=\frac{diameter}{2}=\frac{3in}{2}=1.5in \\ h=6in \end{gathered}[/tex]

Therefore,

[tex]V=\frac{1}{3}\pi(1.5)^2(6)=14.13716\approx14.14[/tex]

Hence, the maximum volume is

[tex]V=14.14in^3[/tex]

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