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If a sphere with radius r is inscribed in a cube with edges of length
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16 Jul 2017, 03:22
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square . Am i correct??
Re: If a sphere with radius r is inscribed in a cube with edges of length
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16 Jul 2017, 03:28
longhaul123 wrote:
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square . Am i correct??
Yes. In geometry "inscribed" means drawing one shape inside another so that it just touches. It does not mean just inside.
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Re: If a sphere with radius r is inscribed in a cube with edges of length
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16 Jul 2017, 06:43
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longhaul123 wrote:
Can someone please explain why the edge of the cube must be equal to the diameter of the sphere? Is it because the inscribed sphere must touch all the points on the square. Am I correct??
Sure the inscribed circle must touch all the four sides of the Rectangle so the side of the rectangle is same as the diameter. see the images attached that also show circumscribed circle, in this case the diagonal of the rectangle serves and the diameter
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15 Nov 2017, 15:50
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AbdurRakib wrote:
If a sphere with radius r is inscribed in a cube with edges of length e, which of the following expresses the relationship between r and e ?
A. \(r=\frac{1}{2}e\)
B. r = e
C. r = 2e
D. \(r=\sqrt{e}\)
E. \(r=\frac{1}{4}e^2\)
Since the sphere is inscribed in the cube, the length of an edge of the cube = the diameter of the sphere. Recall that the diameter is twice the radius. Thus, e = 2r, or 1/2e = r.
Answer: A
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