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?

Question

Athena Middleton

Mathematics

13 January, 02:01

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?

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Kiana Blevins · 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