Answered

Connect with a global community of experts on IDNLearn.com. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.

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

#SPJ1

We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.