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a sphere and a cone have the same volume. each figure has a radius of 3 inches.
what is the height of the cone?

Sagot :

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The volume of a sphere - [tex]\frac{4}{3} \pi r^3[/tex]
The volume of a cone - [tex]\frac{1}{3} \pi r^2 h[/tex]
r - radius, h - height

The sphere and the cone have the same volume and the radius is 3 inches.
[tex]\frac{4}{3} \pi \times 3^3=\frac{1}{3} \pi \times 3^2 \times h \ \ \ |\div \pi \\ \frac{4}{3} \times 27=\frac{1}{3} \times 9 \times h \\ 36=3h \ \ \ |\div 3 \\ h=12[/tex]

The height of the cone is 12 inches.
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