The area of a circle drawn with its diameter as the diagonal of a cube of side of length 1 cm each is :
- $\displaystyle \frac{4\pi }{3}sq\, cm$
- $\displaystyle \frac{3\pi }{2}sq\,cm$
- $\displaystyle \frac{3\pi }{4}sq\,cm$
- $\displaystyle \frac{2\pi }{3}sq\, cm$
The diagonal of a cube with side 1 is sqrt(1^2 + 1^2 + 1^2) = sqrt(3). This is the diameter of the circle. Radius r = sqrt(3)/2. Area = pi * r^2 = pi * (sqrt(3)/2)^2 = pi * (3/4) = 3pi/4.
Using the cube diagonal formula, the diagonal of a cube with side length 1 cm is the square root of 3 multiplied by 1, which equals the square root of 3 cm. Since this diagonal serves as the diameter of the circle, the radius of the circle is half of that, measuring the square root of 3 divided by 2 cm. Applying the area of a circle formula gives pi multiplied by the square of the square root of 3 divided by 2, resulting in an area of 3 times pi divided by 4 square centimeters.