Another Easy Question???

Question

Three right circular cones of radius 1 and height 2 sitting with their points on a plane and their top mutually tangent. What is the radius of the sphere that is mutually tangent to the plane and 3 cones?

Answer 1

Nagpapatawa ba kayo?

The radius of the sphere is (sqrt(15) - sqrt(3)) / 3

Answer 2

1

Answer 3

You can simplify the problem by converting it to the 2nd dimension equivalent. Imagine 2 isosceles triangles with base 2 and height 2 sitting with their points on a line and their bases are collinear. You will solve for the radius of the circle tangent to the triangles and the line, and use the radius to solve for the VOLUME.

For a circle to be tangent to the sides of the triangle and the line, these segments must be perpendicular to the corresponding radii of the circle. For the tangent sides of the triangles, the measure is: (by the Pythagorean Theorem)
√(1² + 2²) = √5
The tangent segment of the line measures (by the definition of rectangle) 1 + 1 = 2.
Now if we draw a perpendicular from the midpt of the segment of the line, it passes through the center of the circle. Since the center of the incircle of a triangle intersects the angle bisectors, and the measure of the angles at the bottom of the triangle to the line measures cos‾¹ (1/√5), the bisected angle measures (cos‾¹ (1/√5))/2.
The base measures 1, and the radius measures 1[tan(cos‾¹ (1/√5))/2]
= [√(1 - cos² cos‾¹ (1/√5)]/[cos cos‾¹ (1/√5) + 1]
= √(1 - 1/5)/(1/√5 + 1)
= √(4/5)/(√5/5 + 1)
= (2√5/5)/(√5/5 + 1)
= 2√5/(√5 + 5)
= 2(√5)(√5 - 5)/(5 - 25)
= 2(5 - 5√5)/(-20)
= - (1 - √5)/2
= (√5 - 1)/2

^_^

Answer 4

The radius is 2

Answer 5

A sphere is like an arrow right, ya throw it at things right.
and why would ya want 3 ice cream cones on a plane?
Unless you threw the sphere at the ice cream cones and killed 3 of em.

Answer 6

3 if the cones are all in a line

Answer 7

1? it's mutually tangent!!

Answer 8

Yeah it's easy if I feel liek doing math

Answer 9

I ain't playin games with you man.

Answer 10

got to review my math subject. i forgot all the formulas :D