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

Volume of square prism = base area · height = (2r)^2 · h = 4r^2 h.
Cylinder volume = base area · height = πr^2 · h.

Since πr^2/(4r^2) = π/4, the cylinder’s volume = (π/4) · (4r^2 h) = πr^2 h.

So the correct choice is: (π/4)·(4r^2)(h) = πr^2 h.