SOLUTION: Let A be the ratio of the volume of a sphere to the volume of a cube each of whose face is tangent to the sphere, and let B be the ratio of the surface area of this sphere to the s
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Question 319494: Let A be the ratio of the volume of a sphere to the volume of a cube each of whose face is tangent to the sphere, and let B be the ratio of the surface area of this sphere to the surface area of the cube. Then find the sum A and B.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let A be the ratio of the volume of a sphere to the volume of a cube each of
whose face is tangent to the sphere, and let B be the ratio of the surface
area of this sphere to the surface area of the cube.
Then find the sum A and B.
:
From the description, the sphere is enclosed in a cube
:
Let r = radius of the sphere
then
2r = side of the cube
:
Volume Ratio; sphere/cube
A = =
cancel r^3
A = = = = ; vol ratio
:
Surface area ratio; sphere/cube
B = = =
Cancel 4, and r^2
B =
:
A + B: + = =
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