SOLUTION: a right cylinder is inscribed in a sphere of radius 10.express its volume and surface area as functions of its height,h.
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Question 487606: a right cylinder is inscribed in a sphere of radius 10.express its volume and surface area as functions of its height,h.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Assume the radius of the cylinder is r. Upon drawing the sphere and cylinder, draw a right triangle (with a vertex at the center of the sphere) with legs r and h/2, and hypotenuse 10 (since the distance from the center to the edge of the sphere is 10). This will satisfy the Pythagorean theorem
^2 = 10^2)
Now use the volume and surface area formulas:
and replace your expression for r into each of these.
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