Question : The area of a circle whose radius is the diagonal of a square whose area is $4\;\mathrm{cm^2}$ is:
Option 1: $16\pi\;\mathrm{cm^2}$
Option 2: $4\pi\;\mathrm{cm^2}$
Option 3: $6\pi\;\mathrm{cm^2}$
Option 4: $8\pi\;\mathrm{cm^2}$

Question

Question : The area of a circle whose radius is the diagonal of a square whose area is $4\;\mathrm{cm^2}$ is:

Option 1: $16\pi\;\mathrm{cm^2}$

Option 2: $4\pi\;\mathrm{cm^2}$

Option 3: $6\pi\;\mathrm{cm^2}$

Option 4: $8\pi\;\mathrm{cm^2}$

Team Careers360 · Accepted Answer

Correct Answer: $8\pi\;\mathrm{cm^2}$

Solution : The area of a square $= s^2$, (where $s$ is the side length of the square.)
Given that the area of the square $=4\;\mathrm{cm^2}$
The side length of the square $=\sqrt{4} = 2\;\mathrm{cm}$
$ herefore$ The diagonal of a square $ = s\sqrt{2}=2\sqrt{2}\;\mathrm{cm}$
This diagonal is the radius of the circle.
The area of a circle $= \pi r^2$, (where $r$ is the radius of the circle.)
$ herefore$ The area of the circle $= \pi (2\sqrt{2})^2 = 8\pi\;\mathrm{cm^2}$
Hence, the correct answer is $8\pi\;\mathrm{cm^2}$.

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Question : The area of a circle whose radius is the diagonal of a square whose area is 4cm2 is:Option 1: 16πcm2Option 2: 4πcm2Option 3: 6πcm2Option 4: 8πcm2

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Question : The area of a circle whose radius is the diagonal of a square whose area is $4 {cm}^{2}$ is:
Option 1: $16 π {cm}^{2}$
Option 2: $4 π {cm}^{2}$
Option 3: $6 π {cm}^{2}$
Option 4: $8 π {cm}^{2}$