Answer to Question #146775 in Geometry for RED

Question

A right circular cone is inscribed in a cube having a diagonal which
measures 20√3 cm.
Altitude of the cone = 20 cm
Volume of the cone = 2094.4 cubic centimeter
Surface Area of the cone = 942.5 cm squared
1. What is the volume of the space between the cone and the cube?

Answer 1

Firstly, we need to clarify the side of cube by it`s diagonal. if we consider a as a side of the cube,

then a²+2*(a)²=d² this came from Pythagoras`s theorem.

In this case, a=20 cm.

Let`s continue the space between cube and cone:

V_space=V_cube-V_cone,

V_cone is already given and we find V_cube =a³ through this form.

Let`s put above :

V_space = a³-2094.4cm³=20³-2094.4=5905.6 cm³.

Answer:5905.6 cm³.