Answer:
[tex]V(t)=\dfrac{32}{81}\pi t^6[/tex]
Step-by-step explanation:
You are given two functions
[tex]V(r)=\dfrac{4}{3}\pi r^3\\ \\r(t)=\dfrac{2}{3}t^2[/tex]
You have to find the volume V as a function of the time t. Substitute the expression of r into the function V(r) to get V(t):
[tex]V(t)\\ \\=\dfrac{4}{3}\pi\cdot \left(\dfrac{2}{3}t^2\right)^3\\ \\=\dfrac{4}{3}\pi \cdot \dfrac{2^3}{3^3}(t^2)^3\\ \\=\dfrac{4}{3}\pi\cdot \dfrac{8}{27}t^6\\ \\=\dfrac{32}{81}\pi t^6[/tex]
