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1. Engr Thomas Pendot wants to construct a frustum from a right circular cone. At what distance from the base of the right circular cone must a plane be passed parallel to the base in order that the volume of his frustum formed shall be three-fifths of the volume of the given cone?

 

2. A cylindrical glass 5 inches in diameter and 8 inches in altitude is filled with iced tea. It is then titled to a position enough for the iced tea level to coincide with the center of the base. How much iced tea is drained from the glass?

 Mar 3, 2021
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1. The part cut off of the frustum will be 2/5 of the original cone, so the smaller cone is$\frac{2h\pi r^2}{15}$ of the original cone, so the smaller cone's height is $^3\sqrt{\frac25}$, so the height is $\boxed{\frac{^3\sqrt5-^3\sqrt2}{^3\sqrt5}}$ of the original cone.

 Mar 3, 2021

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