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Volumes with Cross Sections

AP Calculus AB· difficulty 4/5

The base of a solid is the disk x2+y2≤1x^2+y^2 \le 1. Cross sections perpendicular to the x-axis are squares. The volume is

  • A

    163\frac{16}{3}

    check_circle
  • B

    43π\frac{4}{3}\pi

  • C

    π\pi

  • D

    83\frac{8}{3}

Explanation

Side length at xx: 21−x22\sqrt{1-x^2}. Area: 4(1−x2)4(1-x^2). V=∫−114(1−x2) dx=4[x−x3/3]−11=8(1−1/3)=16/3V = \int_{-1}^1 4(1-x^2)\,dx = 4[x - x^3/3]_{-1}^1 = 8(1-1/3) = 16/3.

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