McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
5. Volumes of Pyramids and Cones
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Exercise 38 Page 846

Use the formula for the volume of a cone, and for the volume of a cylinder.

1704 cubic centimeters. See solution.

Practice makes perfect

We know that the volume of a cone is 568 cubic centimeters. We are asked to find the volume of a cylinder that has the same radius and height as the cone.

Let's analyze the formula for the volume of a cone and for the volume of a cylinder. \begin{gathered} V_\text{cone}=\dfrac{1}{3}\textcolor{darkorange}{Bh} \\ V_\text{cylinder}=\textcolor{darkorange}{Bh} \end{gathered} Notice that if the cylinder and the cone have the same base and the same height, we can substitute V_\text{cylinder} for Bh into the formula for the volume of cone.

V_\text{cone}=\dfrac{1}{3}\textcolor{darkorange}{Bh}
V_\text{cone}=\dfrac{1}{3}V_\text{cylinder}
3V_\text{cone}=V_\text{cylinder}
V_\text{cylinder}=3V_\text{cone}

Therefore, the volume of the cylinder is three times the volume of the cone. Since V_\text{cone}=\textcolor{darkviolet}{568} cubic centimeters, we get that V_\text{cylinder}=3\cdot\textcolor{darkviolet}{568}=1704 cubic centimeters.