You work in the packaging department of a company that makes soup. The old soup can is 4 inches high and has a diameter of 3 inches. Your department is asked to design a bigger soup can that will hold one-and-a-half times as much soup as the old can. Find the height of the bigger soup can if the diameter stays the same.

The height of the new can will be ...... in?

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calculista calculista · Answer 1 · 2019-07-17T16:53:10+02:00

Answer:

[tex]h=6\ in[/tex]

Step-by-step explanation:

step 1

Find the volume of the old can

The volume of the can is equal to

[tex]V=\pi r^{2} h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=4\ in[/tex]

substitute

[tex]V=\pi (1.5)^{2}(4)[/tex]

[tex]V=9\pi\ in^{3}[/tex]

step 2

Find the volume of the bigger can

Multiply the old volume by 1 1/2

[tex]1\frac{1}{2}=1.5[/tex]

so

[tex]V=(1.5)*9\pi\ in^{3}[/tex]

[tex]V=13.5\pi\ in^{3}[/tex]

step 3

Find the height of the bigger can

we have

[tex]V=13.5\pi\ in^{3}[/tex]

[tex]r=1.5\ in[/tex]

substitute in the formula

[tex]13.5\pi=\pi (1.5)^{2}(h)[/tex]

[tex]h=13.5/(1.5)^{2}[/tex]

[tex]h=6\ in[/tex]