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The diagram shows a cube with edges of length x cm and a sphere of radius 3cm

The Diagram Shows A Cube With Edges Of Length X Cm And A Sphere Of Radius 3cm class=

Sagot :

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

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