How many cubic feet are in the volume of a round swimming pool which is 16 feet in diameter and 4 feet deep throughout? Express your answer in terms of $\pi$.
The radius of this pool is $16/2=8$ feet; the volume of this pool is thus $\pi(8^2)(4)=\boxed{256\pi}$ cubic feet.
256\pi
Level 2
Geometry
Problem: How many cubic feet are in the volume of a round swimming pool which is 16 feet in diameter and 4 feet deep throughout? Express your answer in terms of $\pi$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To find the volume of a round swimming pool, we need to use the formula for the volume of a cylinder, which is given by V = πr²h, where r is the radius and h is the height (or depth in this case). 

First, we determine the radius of the pool. The diameter of the pool is 16 feet, so the radius r is half of the diameter: r = 16 feet / 2 = 8 feet.

Next, we identify the depth of the pool, which is given as 4 feet. This depth will serve as the height h in our volume formula.

Now we can substitute the values of r and h into the volume formula:

V = π(8 feet)²(4 feet).

Calculating the area of the base, we find:

(8 feet)² = 64 square feet.

Now, substituting this back into the volume formula gives:

V = π(64 square feet)(4 feet).

Next, we multiply 64 square feet by 4 feet:

64 square feet * 4 feet = 256 cubic feet.

Finally, we combine this with π to express the volume in terms of π:

V = 256π cubic feet.

Thus, the final answer is 256π.<|END_OF_LATENT|> The final answer is $256\pi$.