Answer:
The area of the base of the cylinder is
![14.5\ in^(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/6so7d64lb76o3jzdz65a01i7fgnr22lct7.png)
Explanation:
we know that
The volume of the cylinder is equal to
![V=Bh](https://img.qammunity.org/2020/formulas/mathematics/college/1z8biyc5dxidzjd7gaahhzli35rckolci0.png)
where
B is the area of the base of cylinder
h is the height of the cylinder
In this problem we have
![V=174\ in^(3)](https://img.qammunity.org/2020/formulas/mathematics/high-school/s8eg7f87xkc5bpw4616ugl6i9vlbl8lvid.png)
![h=12\ in](https://img.qammunity.org/2020/formulas/mathematics/middle-school/qudngenixrvgx0bmua85jm5m17ztuztnys.png)
Substitute in the formula and solve for B
![174=B(12)](https://img.qammunity.org/2020/formulas/mathematics/high-school/2mgoedpxt086qh1c7z9zbey1goq4jgnu0h.png)
Apply the division property of equality
![B=174/(12)=14.5\ in^(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/x613hh2jhij5p0gzoxc1fwlujotyrp14v0.png)