Volumes with Cross Sections

AP Calculus AB· difficulty 3/5

Solid has base bounded by y=xy = \sqrt x and y=0y = 0 on [0,4][0, 4]. Cross-sections perpendicular to xx-axis are rectangles of height 22. Volume:

  • A

    1616

  • B

    323\tfrac{32}{3}

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  • C

    88

  • D

    163\tfrac{16}{3}

Explanation

Width =x= \sqrt x, height =2= 2. V=042xdx=216/3=32/3V = \int_0^4 2\sqrt x\,dx = 2 \cdot 16/3 = 32/3.

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