Tag Archives: sphere

Ball and Cube

Suppose that the volume of a ball is equal to times the volume of a cube. What is the ratio of the surface area of the ball to that of the cube? Source: NCTM Mathematics Teacher, September 2006 Solution Let … Continue reading

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Sphere and Cube

A sphere of radius and a cube of edge length have the same total surface area. Find in terms of . Source: NCMT Mathematics Teacher, February 2006 SOLUTION Surface area of sphere = Surface area of cube = Answer: square … Continue reading

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Ice-Cream Cone

An ice-cream cone’s height is three times its diameter. Two spherical scoops of ice cream with the same diameter as the cone are packed into the cone, filling it completely. Some ice cream bulges above the cone’s top. What percent … Continue reading

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Snowman

A family builds a snowman with three perfectly rolled spheres. If the radii of the three spheres are in geometric progression and if the top sphere has a radius of in. and the bottom sphere has a radius of in., … Continue reading

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Circle Sphere

A sphere of radius m is intersected by a plane passing m from the sphere’s center. What is the area of the circle of intersection of the plane and sphere? Please use for the approximation of . Source: mathcontest.olemiss.edu 4/26/2010 … Continue reading

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Tennis Anyone

Three tennis balls snugly fit in a cylindrical can (perfect right cylinder). The balls touch the side, top and bottom of the plastic can. What is the ratio of the volume of the balls to the volume of the space … Continue reading

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