Answer to Question #147432 in Geometry for solid mensuration

Question #147432
A right circular cone is inscribed in a cube having a diagonal which
measures 20 square root of 3 cm.

1. What is the altitude of the cone?
1
Expert's answer
2020-12-01T06:18:08-0500

The diagonal "d" of the cube with the side "a" is


"d^2=a^2+a^2+a^2=3a^2"

"d=\\sqrt{3}a"

Given "d=20\\sqrt{3}\\ cm."

Then


"a=\\dfrac{d}{\\sqrt{3}}=\\dfrac{20\\sqrt{3}}{\\sqrt{3}}=20(cm)"

The radius "r" of the circle inscribed in the square with the side "a" is


"r=\\dfrac{a}{2}"

Then we have the right circular cone inscribed in a cube with the side "a"


"radius=r=\\dfrac{a}{2}, \\ height=h=a"

"h=20\\ cm"

The altitude of the cone is 20 cm.


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