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

A ( Top Left)

Explanation:

Answer 2

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

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 + (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)((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:

`(h)/(1.25)\\=(h)/((5)/(4))\\=h*(4)/(5)\\=h*(0.8)`

Thus, height needs to be
`(4)/(5)` of original (or 80% of original)