Question

To keep cylindrical flower vases from spilling, a designer is planning to enlarge the original area of the base by 25%. The new vase should have the same volume as the original. How should the designer change the height of the vase?

Answer 1

Answer:

To keep the same volume, the designer needs to decrease the height of the vase by 20%

Step-by-step explanation:

Volume of cylinder formula is  $V=\pi r^2 h$

Area of base is  $\pi r^2$, if this area is increased by 25%, the new area of base would be:

$\pi r^2 + \frac{25}{100}(\pi r^2)\\=\pi r^2 + (0.25)(\pi r^2)\\=1.25\pi r^2$

Since volume would be same, we can make the height as:

$V=\pi r^2 h\\V=(1.25\pi r^2)(\frac{h}{1.25})\\V=\pi r^2h$

Thus, we can see that the height needs to be divided by 1.25, which we can write in fractional form as:

$\frac{h}{1.25}\\=\frac{h}{\frac{5}{4}}\\=h*\frac{4}{5}\\=h*(0.8)$

Thus, height needs to be $\frac{4}{5}$ of original (or 80% of original)