Question

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​

Answer 1

The volume of the new can is
`V_2=160x^3\pi\ cm^3`

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

`z=x`

The volume of the original can is

`V_1=\pi r^(2)h`

The volume of the new can is

`V_2=z^(3)V_1`

`V_2=x^3(\pi r^(2)h)`

we have

`r=4\ cm\\h=10\ cm`

substitute

`V_2=x^3(\pi (4)^(2)10)`

`V_2=160x^3\pi\ cm^3`