Question

A construction company was contracted to build a cylindrical storage tank with a diameter of 48 feet and height of 25 feet. Just before construction was to begin, it was learned that a new law allows tanks to be a maximum of 9 feet in height. If the tank is redesigned to meet the law, but has the same volume, what is its new diameter?

Answer 1

v=hpir^2
d/2=r

so, at first, diameter is 48ft
48/2=24ft is radius
height is 25ft

so volume=25pi24^2 or 14400pi cubic feet

max of 9ft

if we want 9ft height
find r
hmm

14400pi=9pir^2
divide both sides by 9pi
1600=r^2
sqrt both sides
40=r
2r=d
2(40)=80=d

the new diameter is 80ft