a solid metallic right circular cone 20 cm high with vertical angle 60 is cut into two parts at the middle point of its height by a plane parallel to the base. its frustum, so obtained be drawn into a wire if diameter 1/16 cm, find the length of the wire .
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The ratio of the top to bottom of a cone, when divided by a plane parallel to the base in a right cone is;
1:7
Using trigonometry, we get that the radius at the base of the triangle is 34.641.
Volume of whole cone is;
V=277127.7416π
The volume of the frustrum of the cone is
Vf=7V/8=242486.774π
This volume is remelted into a cyinder of radius 1/32 cm.
The volume of this cylinder is 242486.774π cm^3.
Substituting the values into the formula;
Vc=πhr^2
We get;
h=242486.774π/π(1/32)^2
h=248306456.5cm
1:7
Using trigonometry, we get that the radius at the base of the triangle is 34.641.
Volume of whole cone is;
V=277127.7416π
The volume of the frustrum of the cone is
Vf=7V/8=242486.774π
This volume is remelted into a cyinder of radius 1/32 cm.
The volume of this cylinder is 242486.774π cm^3.
Substituting the values into the formula;
Vc=πhr^2
We get;
h=242486.774π/π(1/32)^2
h=248306456.5cm
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