Question

1. how many gallons will a 40 foot tall tank with a circumference of 283 feet hold when it is full?

Explanation:

Step1: Find the radius from the circumference

The formula for the circumference of a circle is \( C = 2\pi r \), so we can solve for \( r \): \( r=\frac{C}{2\pi} \). Given \( C = 283 \) feet, \( r=\frac{283}{2\pi}\approx\frac{283}{6.2832}\approx45.04 \) feet.

Step2: Calculate the volume of the cylindrical tank

The volume \( V \) of a cylinder is \( V=\pi r^{2}h \), where \( h = 40 \) feet (height of the tank). Substituting \( r\approx45.04 \) and \( h = 40 \): \( V=\pi\times(45.04)^{2}\times40\approx\pi\times2028.6\times40\approx\pi\times81144\approx254968.15 \) cubic feet.

Step3: Convert cubic feet to gallons

We know that 1 cubic foot is approximately 7.48052 gallons. So, the number of gallons \( G = V\times7.48052 \). Substituting \( V\approx254968.15 \): \( G\approx254968.15\times7.48052\approx1907300 \) (rounded to a reasonable approximation).

Answer:

Approximately 1907300 gallons (the value may vary slightly depending on the precision of \( \pi \) and the conversion factor used)