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Rodney's Cheese Slice

GMAT-1AEJFO

Rodney has a wheel of sharp cheddar cheese that he wishes to slice and arrange on a dinner platter. He slices out a perfect third of the cheese wheel, by cutting two $10$ inch cuts from the edge of the wheel to the exact center of the wheel.

If the cheese wheel is $4$ inches thick, what is the volume of Rodney's cheese slice?

A

$\cfrac{200π}{3}$

B

$\cfrac{400π}{6}$

C

$\cfrac{400π}{\sqrt2}$

D

$\cfrac{800π}{3}$

E

$\cfrac{400π}{3}$