Calculus

The base of a solid is the circle x^2 + y^2 = 9. Cross sections of the solid perpendicular to the x-axis are squares. What is the volume, in cubic units, of the solid?

A. 18
B. 36
C. 72
D. 144

Please help. Thank you in advance.

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  1. the solid is symmetric, so you just find the volume of the right side and double it.

    Think of the solid as a stack of thin square sheets of thickness dx. The base of each square sheet has side 2y, where y = √(9-x^2), so its area is 4y^2=4(9-x^2)

    Now just integrate to add up the volumes of all those thin squares.

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    oobleck
  2. Okay, so for the integral, I got 4(9x- 1/3x^3) + C.

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  3. so for x=3, volume= 4(27-9)=4(18)=72

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    bobpursley
  4. actually, you forgot to double it. You found the volume of the right half only.
    v = ∫[-3,3] 4(9-x^2) dx = 2∫[0,3] 4(9-x^2) dx = 144

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    oobleck

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