jmc

Question

P.J. has a cylindrical mug with a 3-inch diameter. His mug is filled to a height of 6 inches with grape juice. Schuyler has a cylindrical mug with a 4-inch diameter. To what height in inches must Schuyler's mug be filled so that he receives the same amount of juice as P.J.? Express your answer as a mixed number.

Accepted Answer

P.J.'s juice fills up a cylinder with radius 3/2 inches and height 6 inches; his juice has volume

π (\frac{3}{2})^{2} (6) = \frac{27 π}{2}

cubic inches.

Schuyler's juice fills up a cylinder with radius 2 inches and unknown height

h

inches; his juice has volume

π (2^{2}) (h) = 4 π h

cubic inches. Setting this equal to P.J.'s volume and solving for

h

yields

\frac{27 π}{2} = 4 π h \Rightarrow h = \frac{27}{8} = 3 \frac{3}{8}

inches.