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Arturiano [62]
3 years ago
5

A sphere and a cube have equal surface areas. The length of one edge of the cube is 1.11 meters. What is the radius of the spher

e?
Mathematics
1 answer:
Nady [450]3 years ago
3 0

Answer:

  0.767 m

Step-by-step explanation:

The area of a cube of edge length s is given by ...

  A = 6s^2

The area of a sphere of radius r is given by ...

  A = 4πr^2

When these two are equal, we have ...

  6s^2 = 4πr^2

  r^2 = 6s^2/(4π)

  r = s·√(3/(2π)) ≈ s·0.690988

The radius of the sphere is about ...

  r ≈ 0.690899×1.11 m

  r ≈ 0.767 m . . . . approximate sphere radius

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