Answer:
4 yards
Step-by-step explanation:
The formula to determine the volume of the cylinder is the area of the circle (base of cylinder) multiplied by the height of the cylinder.
[tex]\rightarrow \pi r^{2} h = \text{Volume of cylinder}[/tex]
Substitute the height and the volume of the cylinder into the formula:
[tex]\rightarrow \pi r^{2} h = \text{Volume of cylinder}[/tex]
[tex]\rightarrow \pi (r^{2})( 4) = 64\pi[/tex]
Divide both sides by π and simplify:
[tex]\rightarrow \dfrac{\pi (r^{2})( 4)}{\pi } = \dfrac{64\pi}{\pi }[/tex]
[tex]\rightarrow { (r^{2})( 4)} = 64[/tex]
Divide both sides by 4 and simplify:
[tex]\rightarrow { \dfrac{(r^{2})( 4)}{4} } = \dfrac{64}{4}[/tex]
[tex]\rightarrow {{(r^{2}) = 16[/tex]
Take square root both sides and simplify:
[tex]\rightarrow \sqrt{r^{2}} = \sqrt{16}[/tex]
[tex]\rightarrow \sqrt{r \times r} = \sqrt{4 \times 4}[/tex]
[tex]\rightarrow r = 4 \ \text{yards}[/tex]
The radius of the base is 4 yards.
