Q:
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.
Consider the following statements:
1) The surface area of the sphere is √5 Times the curved surface area of the cone.
2) The surface area of the cube is equal to the curved surface area of the cylinder. Which of the above statements is/are correct?
Answer & Explanation
Answer: D) Neither 1 nor 2
Explanation:
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)
Thus neither 1 nor 2 are true
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