Before using the 80%, first find the volume of the tank if it were completely full using $r = 5$ feet, $h = 12$ feet, and the formula $V = \pi r^2 h$.

Once you know the full volume, how do you find 80% of that amount? How do you write 80% as a decimal?

80% is a bit less than 100%, so your final answer should be somewhat less than the full capacity you computed, and definitely more than half of it.

In Desmos, type the expression 0.8*3.14*5^2*12 and look at the numerical result it returns; that value is the volume of water in the tank (in cubic feet).

A cylindrical tank’s volume is the area of its circular base times its height.

The formula is

where $r$ is the radius and $h$ is the height.

For this tank:

• $r = 5$ feet
• $h = 12$ feet

First, we will find the tank’s full capacity (its total interior volume).

Substitute $r=5$ and $h=12$ into the formula:

Now simplify step by step:

• $5^2 = 25$
• $25 \times 12 = 300$
• $\pi r^2 h = 3.14 \times 300 = 942$

So the tank’s full capacity is $942$ cubic feet when completely full.

The tank is filled to 80% of its capacity, so we need $80\%$ of $942$.

Convert $80\%$ to a decimal: $80\% = 0.8$.

Compute $0.8 \times 942$:

Therefore, the volume of water inside the tank is 753.6 cubic feet, which corresponds to answer choice C.