Question

the diameter of a cylindrical water tank is 9 ft, and its height is 7 ft. answer the parts below. make sure that you use the correct units in your answers. if necessary, refer to the list of geometry formulas. (a) find the exact volume of the tank. write your answer in terms of π. exact volume: (b) using the aleks calculator, approximate the volume of the tank. to do the approximation, use your answer to part (a) and the π button on the calculator. round your answer to the nearest hundredth. approximate volume:

Explanation:

Step1: Find the radius

The diameter $d = 9$ ft, so the radius $r=\frac{d}{2}=\frac{9}{2}$ ft.

Step2: Use the cylinder - volume formula

The volume formula for a cylinder is $V=\pi r^{2}h$. Given $h = 7$ ft and $r=\frac{9}{2}$ ft, we substitute these values into the formula: $V=\pi\times(\frac{9}{2})^{2}\times7=\pi\times\frac{81}{4}\times7=\frac{567\pi}{4}$ $ft^{3}$.

Step3: Approximate the volume

Using $\pi\approx3.14$, we have $V=\frac{567\times3.14}{4}=\frac{1780.38}{4}=445.095\approx445.10$ $ft^{3}$.

Answer:

(a) $\frac{567\pi}{4}$ $ft^{3}$
(b) $445.10$ $ft^{3}$