bradythomaschefsky
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A company wants to increase the size of its spherical containers. The new volume N is equal to the old volume V times the scale factor F cubed or N=4/3*x*r^3*F^3 . Find the scale factor F if the radius of the older container is 2 feet and that of the new container is 6 feet.

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  • That x is Ο€

[tex]\\ \rm\Rrightarrow N=\dfrac{4}{3}\pi r^3F^3[/tex]

[tex]\\ \rm\Rrightarrow \dfrac{4}{3}\pi (r_2)^3=\dfrac{4}{3}\pi (r_1)^3F_3[/tex]

  • Cancel 4/3 Ο€

[tex]\\ \rm\Rrightarrow r_2^3=r_1^3F^3[/tex]

[tex]\\ \rm\Rrightarrow F^3=\dfrac{r_2^3}{r_1^3}[/tex]

[tex]\\ \rm\Rrightarrow \sqrt[3]{F^3}=\sqrt[3]{\dfrac{r_2^3}{r_1^3}}[/tex]

[tex]\\ \rm\Rrightarrow F=\dfrac{r_2}{r_1}[/tex]

[tex]\\ \rm\Rrightarrow F=\dfrac{6}{2}[/tex]

[tex]\\ \rm\Rrightarrow F=3[/tex]

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