SOLUTION: a cyclider of radius r sits snugly inside a cube. Which of the following expressions represents the difference of their LATERAL AREAS? a)2r^2 (8- pi) b) 2r (pi

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Question 237540: a cyclider of radius r sits snugly inside a cube. Which of the following expressions represents the difference of their LATERAL AREAS?
a)2r^2 (8- pi)
b) 2r (pi - 2)
c) 2r (4- pi)
d) 4r^2 (4- pi)
^2 = squared
Answer by solver91311(12126) (Show Source):
You can put this solution on YOUR website!

If the cylinder with radius fits snugly inside the cube, the cube must have an edge length equal to the diameter of the cylinder, or .

The lateral surface area of a cube is the area of 4 of the sides:

So for this cube:

The lateral surface area of a cylinder is:

But for this cylinder, the height is equal to the edge of the cube, so:

Compute the difference:

John

SOLUTION: a cyclider of radius r sits snugly inside a cube. Which of the following expressions represents the difference of their LATERAL AREAS? a)2r^2 (8- pi) b) 2r (pi - 2) c) 2r