Question

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.

Answer 1

• That x is π

`\\ \rm\Rrightarrow N=(4)/(3)\pi r^3F^3`

`\\ \rm\Rrightarrow (4)/(3)\pi (r_2)^3=(4)/(3)\pi (r_1)^3F_3`

• Cancel 4/3 π

`\\ \rm\Rrightarrow r_2^3=r_1^3F^3`

`\\ \rm\Rrightarrow F^3=(r_2^3)/(r_1^3)`

`\\ \rm\Rrightarrow \sqrt[3]{F^3}=\sqrt[3]{(r_2^3)/(r_1^3)}`

`\\ \rm\Rrightarrow F=(r_2)/(r_1)`

`\\ \rm\Rrightarrow F=(6)/(2)`

`\\ \rm\Rrightarrow F=3`