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PLEASE HELP!
3. A certain can of soup has a radius of 4 cm and a height of 10 cm. For a new can, the height
and the radius will each be increased by x cm. Find the polynomial that gives the volume of the
new can in cm'. Leave your answer in terms of . [Use V = pi r^2h​

Respuesta :

calculista

Answer:

The volume of the new can is [tex]V_2=160x^3\pi\ cm^3[/tex]

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z ----> the scale factor

In this problem

[tex]z=x[/tex]

The volume of the original can is

[tex]V_1=\pi r^{2}h[/tex]

The volume of the new can is

[tex]V_2=z^{3}V_1[/tex]

[tex]V_2=x^3(\pi r^{2}h)[/tex]

we have

[tex]r=4\ cm\\h=10\ cm[/tex]

substitute

[tex]V_2=x^3(\pi (4)^{2}10)[/tex]

[tex]V_2=160x^3\pi\ cm^3[/tex]

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