school
Acemy

Volumes with Cross Sections

AP Calculus AB· difficulty 3/5

Base on [0,1][0, 1], width x\sqrt x. Cross-sections are <strong>equilateral triangles</strong> with side x\sqrt x. Volume?

  • A

    312\tfrac{\sqrt 3}{12}

  • B

    34\tfrac{\sqrt 3}{4}

  • C

    38\tfrac{\sqrt 3}{8}

    check_circle
  • D

    12\tfrac{1}{2}

Explanation

Area =34s2=34x= \tfrac{\sqrt 3}{4} s^2 = \tfrac{\sqrt 3}{4} x. V=∫0134x dx=38V = \int_0^1 \tfrac{\sqrt 3}{4} x\,dx = \tfrac{\sqrt 3}{8}.

Want 10 more like this — adaptive to your weak spots?

Practice 10 like thisarrow_forwardPredict my AP score

Related questions

auto_awesomeAll Toolsquestion_answerHomework Q&Amenu_bookAP & SAT PreptimelineLearn Mode