Answer:
A=78.23in²
Step-by-step explanation:
First we need to solve for the radius. The volume of a cylinder can be found using the formula:
[tex]V=\pi r^{2} h[/tex]
Now we have the variables:
V = 1177.5 in³
h = 15
r = ?
[tex]1177.5=\pi r^{2}15[/tex]
[tex]\dfrac{1177.5}{15}=\dfrac{\pi r^{2} }{15}[/tex]
[tex]78.5=\pi r^{2}[/tex]
[tex]\dfrac{78.5}{\pi }=\dfrac{\pi r^{2} }{\pi }[/tex]
[tex]r^{2}[/tex]≅24.99
[tex]\sqrt{r^{2} }[/tex]≅[tex]\sqrt{24.99}[/tex]
r≅4.99in
Now since we're looking for the area of the base, we can use the formula for the area of a circle which is:
[tex]A=\pi r^{2}[/tex]
[tex]A=\pi (4.99)^{2}[/tex]
A=78.23in²
