The surface area of circle of radius 3 cm and cube of edge length x cm being equal implies [tex]x = \sqrt{k\pi}[/tex] integer (k = 6).
How to find the surface area of a sphere?
Suppose that radius of the considered sphere is of 'r' units.
Then, its surface area S would be:
[tex]S = 4\pi r^2 \: \rm unit^2[/tex]
Given that:
- Side length of considered cube = x cm
- Radius of considered sphere = 3 cm
- Surface area of the considered cube = surface area of the considered sphere.
Finding the surface area of the considered cube and sphere:
- Surface area of cube with x cm edge length = [tex]\rm 6 \times side^2 = 6(x)^2 \: \rm cm^2[/tex]
- Surface area of sphere with radius r = k cm is [tex]4 \pi r^2 = 4\pi (3)^2 = 36\pi \: \rm cm^2[/tex]
Thus, we get:
[tex]6x^2 = 36\pi\\\\\text{Dividing both the sides by 6}\\\\x^2 = 6\pi\\\\\text{Taking root of both the sides}\\\\x = \sqrt{6\pi} \: \rm cm[/tex]
(took positive value out of the root since x cannot be negative as it represents length of the edge of a cube which cannot be a negative quantity).
Thus, the surface area of circle of radius 3 cm and cube of edge length x cm being equal implies [tex]x = \sqrt{k\pi}[/tex] integer (k = 6).
Learn more about surface area of sphere here:
https://brainly.com/question/13250046
#SPJ1
