Volumes Practice Test 3

Concept:Volume of a cylinder is $V=\pi r^2h$, so a change in diameter affects volume as the square of the radius.Explanation:Let original radius be $r$ and height be $h$.Diameter increases by $50\%$, so radius also increases by $50\%$.New radius $= 1.5r$.Let new height be $h'$.Volume remains unchanged, so:$$\pi (1.5r)^2h' = \pi r^2h$$$$2.25r^2h' = r^2h$$$$h' = \frac{h}{2.25} = \frac{4h}{9}$$Decrease in height $= h-\frac{4h}{9}=\frac{5h}{9}$.Percentage decrease $= \frac{5h/9}{h}\times100\% = 55.56\%$.Answer:The height must be decreased by $55.56\%$.Correct option: B.