Question

A cylinder fits inside a square prism as shown. For every cross section, the ratio of the area of the circle to the area of the square is StartFraction pi r squared Over 4 r squared EndFraction or StartFraction pi Over 4 EndFraction.

A cylinder is inside of a square prism. The height of the cylinder is h and the radius is r. The base length of the pyramid is 2 r.

Since the area of the circle is StartFraction pi Over 4 EndFraction the area of the square, the volume of the cylinder equals

StartFraction pi Over 2 EndFraction the volume of the prism or StartFraction pi Over 2 EndFraction(2r)(h) or πrh.
StartFraction pi Over 2 EndFraction the volume of the prism or StartFraction pi Over 2 EndFraction(4r2)(h) or 2πrh.
StartFraction pi Over 4 EndFraction the volume of the prism or StartFraction pi Over 4 EndFraction(2r)(h) or StartFraction pi Over 4 EndFractionr2h.
StartFraction pi Over 4 EndFraction the volume of the prism or StartFraction pi Over 4 EndFraction(4r2)(h) or Pir2h.

Answer 1

The answer is D

Explanation:

Answer 2

StartFraction pi Over 4 EndFraction the volume of the prism or StartFraction pi Over 4 EndFraction(4r^2)(h) or Pi r^2h

Explanation:

When the cross sections are uniform, the ratio of volumes will be the same as the ratio of areas. Since the ratio of the area of the cross section of the cylinder to the area of the cross section of the prism is π/4 for all cross sections, that will be the ratio of volumes of cylinder to prism.

If the volume of the prism is (2r)²h = 4r²h, then the volume of the cylinder will be ...

cylinder volume = (π/4)(4r²h) = πr²h

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Comment on the question

It's a lot easier to make sense of the question and the answers if appropriate math symbols are used instead of words.