A right circular cylinder just encloses a sphere. If p is the surface area of the sphere and q is the curved surface area of the cylinder, then which one of the following is correct?

Option 1 : p = q

Given:

The surface area of the sphere = p

The curved surface area of the cylinder = q

Formula used

Curved surface area of sphere = 4π × (radius)²

Curved surface area of cylinder = 2π × radius × height

Calculation

When a right circular cylinder just encloses a sphere as shown below, the radius of the sphere and cylinder are equal and the height of cylinder is equal to the diameter of the sphere

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Let, radius of sphere = radius of cylinder = r

Here, height of cylinder = 2r

Now,

Curved surface area of sphere = 4π × (radius)²

⇒ p = 4πr²

Curved surface area of cylinder = 2π × radius × height

⇒ q = 2πr × 2r = 4πr²

∴ p = q