McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
4. Volumes of Prisms and Cylinders
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Exercise 35 Page 836

Use the formula for the volume of a cylinder.

About 12 762 720 cubic centimeters

Practice makes perfect
According to the specifications, the diameter of a column can be between 30 and 95 centimeters, and the height of the column is 500 centimeters.

We are asked to find the difference in volume between the largest and the smallest possible column. Let's use the formula for the volume of a cylinder.

Cylinder Smallest Largest
Radius r= 30 r= 95
Height h= 500 h= 500
Volume V=Ď€ r^2 h
\textcolor{darkorange}{V_\text{smallest}}=\pi({\color{#0000FF}{30}})^2({\color{#009600}{500}})=\textcolor{darkorange}{450\,000\pi} \textcolor{darkviolet}{V_\text{largest}}=\pi({\color{#0000FF}{95}})^2({\color{#009600}{500}})=\textcolor{darkviolet}{4\,512\,500\pi}
Now, let's find the difference \textcolor{darkviolet}{V_\text{largest}}-\textcolor{darkorange}{V_\text{smallest}}, and round it to the nearest cubic centimeter.
\textcolor{darkviolet}{V_\text{largest}}-\textcolor{darkorange}{V_\text{smallest}}
â–Ľ
Substitute values and evaluate
4 512 500Ď€-450 000Ď€
4 062 500Ď€
12 762 720.15520853...
12 762 720
Therefore, the difference is about 12 762 720 cubic centimeters.