Consider the following statements 1 The surface area of the sphere is 5 Times the curved surface are...........

Quantitative Aptitude (CDS) Mensuration 3D

Direction: Consider the following for the next three (03) items :
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?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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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)
Surface area of Sphere = 4πr1² = 3πa²
Curved Surface area of cone = πr2L = πr2(h2+r2²)^1/2 = √5 πa²/4
Surface area of cube = 6a²
Curved Surface area of cylinder = 2πr2h = πa²
Thus neither 1 nor 2 are true