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

Answer 1

D

Explanation:

i took the test

Answer 2

`\pi r^2 h`

Explanation:

`\text{Area of the circle: Area of the Square =}(\pi r^2)/(4r^2):1=(\pi)/(4):1`

Height of the cylinder =h

Radius of the Cylinder=r

Base Length of the Prism=2r

Therefore:

Volume of the Prism =
`(2r)^2h=4r^2h`

`\text{Volume of the Cylinder =} (\pi)/(4)(\text{the volume of the prism)}\\=(\pi)/(4)(4 r^2 h) \\=\pi r^2 h`