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 dd of the cube with the side aa is


d2=a2+a2+a2=3a2d^2=a^2+a^2+a^2=3a^2

d=3ad=\sqrt{3}a

Given d=203 cm.d=20\sqrt{3}\ cm.

Then


a=d3=2033=20(cm)a=\dfrac{d}{\sqrt{3}}=\dfrac{20\sqrt{3}}{\sqrt{3}}=20(cm)

The radius rr of the circle inscribed in the square with the side aa is


r=a2r=\dfrac{a}{2}

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


radius=r=a2, height=h=aradius=r=\dfrac{a}{2}, \ height=h=a

h=20 cmh=20\ cm

The altitude of the cone is 20 cm.


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