Question

a grain silo has a cylindrical shape. its radius is 7.5 ft, and its height is 35 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 silo. write your answer in terms of π. exact volume: (b) using the aleks calculator, approximate the volume of the silo. 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: Recall cylinder volume formula

The volume formula for a cylinder is $V=\pi r^{2}h$, where $r$ is the radius and $h$ is the height.

Step2: Identify given values

We are given that $r = 7.5$ ft and $h=35$ ft.

Step3: Calculate exact volume

Substitute the values into the formula: $V=\pi\times(7.5)^{2}\times35=\pi\times56.25\times35 = 1968.75\pi$ $ft^{3}$.

Step4: Calculate approximate volume

Using $\pi\approx3.14159$, we have $V\approx1968.75\times3.14159 = 1968.75\times3.14159=6182.35$ $ft^{3}$ (rounded to the nearest hundredth).

Answer:

(a) $1968.75\pi$ $ft^{3}$
(b) $6182.35$ $ft^{3}$