Try this beautiful problem from AMC 10A, 2004 based on Mensuration: Cylinder
A company sells peanut butter in cylindrical jars. Marketing research suggests that using wider jars will increase sales. If the diameter of the jars is increased by \(25\%\) without altering the volume, by what percent must the height be decreased?
Mensuration
Cylinder
Percentage
Answer: \(36\)
AMC-10A (2004) Problem 11
Pre College Mathematics
Let the radius of the jar be \(x\) and height be \(h\).then the volume (V) of the jar be\(V\)= \(\pi (x)^2 h\). Diameter of the jar increase \(25 \)% Therefore new radius will be \(x +\frac{x}{4}=\frac{5x}{4}\) .Now the given condition is "after increase the volume remain unchange".Let new height will be \(h_1\).Can you find out the new height....?
can you finish the problem........
Let new height will be \(H\).Therefore the volume will be \(\pi (\frac{5x}{4})^2 H\).Since Volume remain unchange......
\(\pi (x)^2 h\)=\(\pi (\frac{5x}{4})^2 H\) \(\Rightarrow H=\frac{16h}{25}\).
height decrease =\(h-\frac{16h}{25}=\frac{9h}{25}\).can you find out the decrease percentage?
can you finish the problem........
Decrease Percentage=\( \frac {\frac {9h}{25}}{h} \times 100=36\)%
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