A right circular cylinder's height increases by 96% while its radius decreases by 25%. What is the approximate percentage change in its volume? Select the nearest integer.
10% increase
The volume of a right circular cylinder is \(V = \pi r^2 h\), so any change in radius and height changes the volume in proportion to \(r^2 h\).
The height increases by 96%, so the new height factor is \(1 + 0.96 = 1.96\).
The radius decreases by 25%, so the new radius factor is \(1 - 0.25 = 0.75\).
Since volume depends on \(r^2\), the radius contributes a factor of \((0.75)^2 = 0.5625\).
New volume factor \(= 0.5625 \times 1.96 = 1.1025\).
Percentage change \(= (1.1025 - 1)\times 100 = 10.25\%\), an increase.
Rounding to the nearest integer gives about a 10% increase.
The volume increases by approximately 10%.
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