Re: Sphere, Geometry Problem

If youcut the cone in two halves, you will get an equilateral triangle its vertices are vertices of an hexagon and its height is 3R/2 and R is the radius of the sphere. Continue from there

Re: Sphere, Geometry Problem

cone has an equilateral cross section side length d

altitude ofcone =1/2drad3

radius ofsphere=1/2 d/rad3

volume of cone /volume sphere wiil cancel out to 9/4

Re: Sphere, Geometry Problem

I'm still confused. Is the radius of the sphere equal to the radius of the cone?

Thanks for replying i appreciate your feedbacks

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Re: Sphere, Geometry Problem

Quote:

Originally Posted by

**PhillipMasagca** I'm still confused. Is the radius of the sphere equal to the radius of the cone?

Thanks for replying i appreciate your feedbacks

No it is not. Use the information in the attached and use the properties of an equilateral triangle.

Attachment 29228

Re: Sphere, Geometry Problem

Quote:

Originally Posted by

**PhillipMasagca** I'm still confused. Is the radius of the sphere equal to the radius of the cone?

Thanks for replying i appreciate your feedbacks

look closely at the values I gave you for base radius and sphere radius and note they are not equal to each other

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Re: Sphere, Geometry Problem

Quote:

Originally Posted by

**bjhopper** look closely at the values I gave you for base radius and sphere radius and note they are not equal to each other

My apology. the center of an inscribed circle is the intersection point of the bisectors. In an equilateral triangle a bisector is also a median. The intersection point of the bisectors is also the intersection point of the medians. Therefore, in your problem the radius of the inscribed circle is 1/3 the length of the median, which is also the height of the equilateral triangle. You need to correlate the side of the triangle with the radius of the circle via the length of the height.

Attachment 29234

Re: Sphere, Geometry Problem

@bjhopper what is 1/2drad3? is it 1/2(diameter)(radius^3)?? (Thanks Again)

@votan after i get the radius of the sphere to be 1/3 of the height of the cone what is the next step. im kinda confused (Thanks Again)

Re: Sphere, Geometry Problem

Quote:

Originally Posted by

**PhillipMasagca** @bjhopper what is 1/2drad3? is it 1/2(diameter)(radius^3)?? (Thanks Again)

@votan after i get the radius of the sphere to be 1/3 of the height of the cone what is the next step. im kinda confused (Thanks Again)

I decipher 1/2drad3 as (1/2)*diameter*radical(3), radical here means sqrt

You got the radius of the sphere correctly assuming the height of the cone is one unit. but if you label the height of the cone h units, What the radius of the sphere would be.

Now you will need to relate h to the side of the equilateral triangle, which is the base of the triangle (why?)

Re: Sphere, Geometry Problem

Quote:

Originally Posted by

**PhillipMasagca** @bjhopper what is 1/2drad3? is it 1/2(diameter)(radius^3)?? (Thanks Again)

@votan after i get the radius of the sphere to be 1/3 of the height of the cone what is the next step. im kinda confused (Thanks Again)

1/2 *d*rad3 = alt of cone

1/2 *d /rad3 = radius of sphere

Both are properties of 30-60-90 triangles

Re: Sphere, Geometry Problem

Quote:

Originally Posted by

**bjhopper** 1/2 *d*rad3 = alt of cone

1/2 *d /rad3 = radius of sphere

Both are properties of 30-60-90 triangles

Radius of sphere is third altitude of cone. The sphere is inscribed in the cone.

Re: Sphere, Geometry Problem

Quote:

Originally Posted by

**votan** Radius of sphere is third altitude of cone. The sphere is inscribed in the cone.

1/2*d*1/rad3 = radius of sphere = 1/3 of alt of cone

1/2*d*1/rad 3=1/2*d*rad3/rad3^2=1/6*d*rad3=1/3*d*1/2*rad3

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Re: Sphere, Geometry Problem