Answer:
[tex]r = \sqrt[3]{7.5 t/\pi} \\[/tex]
Step-by-step explanation:
Given volume as a function of time is for a ball is V(t) = 10t
we know that volume of a sphere is given by [tex](4/3) *\pi * r^3[/tex]
where r is radius of sphere
Note we are using formula for sphere as ball is spherical in shape
Now equating volume V(t) = 10t, and volume of a sphere is given by formula [tex](4/3) *\pi * r^3[/tex]
[tex]10t = (4/3 ) \pi r^3\\=> 10t * 3/4 = \pi r^3\\=>(10t * (3/4))/\pi = r^3\\=> r^3= (30/4)*t /\pi = 7.5 t/\pi \\=> r = \sqrt[3]{7.5 t/\pi} \\\\or \\ r = ({7.5 t/\pi})^1/3[/tex]
Hence radius at a given volume can be modeled by function
[tex]=> r = \sqrt[3]{7.5 t/\pi} \\\\\\[/tex]
