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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

Respuesta :

Answer:

[tex]\pi r^2 h[/tex]

Step-by-step explanation:

[tex]\text{Area of the circle: Area of the Square =}\dfrac{\pi r^2}{4r^2}:1=\dfrac{\pi}{4}:1[/tex]

Height of the cylinder =h

Radius of the Cylinder=r

Base Length of the Prism=2r

Therefore:

Volume of the Prism =[tex](2r)^2h=4r^2h[/tex]

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

Answer:

D

Step-by-step explanation:

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