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Area and Volume

SAT Math· difficulty 5/5

A grain silo is a cylinder of radius 44 and height 2020 topped by a hemisphere of radius 44. What is the total volume?

  • A

    320π+2563π320\pi+\frac{256}{3}\pi

  • B

    80π+1283π80\pi+\frac{128}{3}\pi

  • C

    320π+1283π320\pi+\frac{128}{3}\pi

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  • D

    320π+64π320\pi+64\pi

Explanation

Cylinder =π(16)(20)=320π=\pi(16)(20)=320\pi. Hemisphere =12⋅43π(64)=1283π=\frac{1}{2}\cdot\frac{4}{3}\pi(64)=\frac{128}{3}\pi. Total =320π+1283π=320\pi+\frac{128}{3}\pi.

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