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  [tex]V=\pi r^2 h[/tex]
Area of base is  [tex]\pi r^2[/tex], if this area is increased by 25%, the new area of base would be:
[tex]\pi r^2 + \frac{25}{100}(\pi r^2)\\=\pi r^2 + (0.25)(\pi r^2)\\=1.25\pi r^2[/tex]
Since volume would be same, we can make the height as:
[tex]V=\pi r^2 h\\V=(1.25\pi r^2)(\frac{h}{1.25})\\V=\pi r^2h[/tex]
Thus, we can see that the height needs to be divided by 1.25, which we can write in fractional form as:
[tex]\frac{h}{1.25}\\=\frac{h}{\frac{5}{4}}\\=h*\frac{4}{5}\\=h*(0.8)[/tex]
Thus, height needs to be [tex]\frac{4}{5}[/tex] of original (or 80% of original)
