Answer:
[tex]\sqrt[3]{3140^2\pi}\approx 146.41\ ft^2[/tex]
Step-by-step explanation:
The volume of the cylinder is
[tex]V_{cylinder}=\pi r^2\cdot H,[/tex]
where r is the base radius and H is the height.
Since [tex]H=\dfrac{1}{2}r[/tex] and V=1570 cubic feet, then
[tex]1570=\pi r^2\cdot \dfrac{r}{2},\\ \\1570=\dfrac{\pi r^3}{2},\\ \\r^3=\dfrac{3140}{\pi},\\ \\r=\sqrt[3]{\dfrac{3140}{\pi}}\ ft.[/tex]
The area of its bottom floor is
[tex]A_{floor}=\pi r^2=\pi\cdot \left(\sqrt[3]{\dfrac{3140}{\pi}}\right)^2= \sqrt[3]{3140^2\pi}\approx 146.41\ ft^2.[/tex]
