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A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What is the ratio of the volume of the sphere to that of cone?

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular once is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. What is the ratio of the volume of the sphere to that of cone? Correct Answer 6\u221a3:1

The top view of the given assembly will look like the figure above Outermost is the sphere. Inside that there is a cube and within that there is a cone and cylinder with same radius. Here side of cube = a Diameter of Sphere = body diagnol = √3 a Radius of sphere = √3 a/2 =r1 Height of Cylinder = Height of cone = side of cube = a =h Radius of cylinder = Radius of cone = side of cube/2 = a/2 =r2(as shown in the figure) Volume of sphere/volume of cone = 43πr1313πr22h = 6√3:1

Related Questions

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