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Mathematics

Assertion (A): The surface area of largest sphere that can be inscribed in a hollow cube of side 'a' cm is πa2 cm2.

Reason (R): The surface area of sphere of radius 'r' is 43πr3\dfrac{4}{3}πr^3.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

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Answer

Given, a sphere that can be inscribed in a hollow cube.

The maximum diameter of the sphere that can be inscribed is equal to the side of the cube (a).

The radius of the sphere is half of the diameter: r = a2\dfrac{a}{2}

The surface area of a sphere is given by 4πr2.

So, reason(R) is false.

The surface area of a sphere = 4 x π x (a2)2\Big(\dfrac{a}{2}\Big)^2

= 4 x π x a24\dfrac{a^2}{4}

= πa2 cm2.

So, assertion (A) is true.

Thus, Assertion (A) is true, but Reason (R) is false.

Hence, option 1 is the correct option.

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