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NAME DATE PERIOD Lesson 2 Homework Practice Volume of Cones Find the volume of each cone. Round to the nearest tenth. 1. 2. 3. 4. 5. 6. 7. 8. 9. height: 26.8 centimeters; radius: 12 centimeters 10.

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  4. In the PERIOD section, indicate the class period during which you are completing this assignment. This information assists your instructor in organizing submissions.
  5. Proceed to the volume calculations for each cone listed from 1 to 10, using the provided measurements. Round your answers to the nearest tenth as required.
  6. After completing the volume calculations, move on to finding the area of the base for the cones listed in questions 11 and 12 using the given volumes and heights.
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Fill the cones with water and empty out one cone at a time. Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.

The cone which has the same base radius and height will have the same base area but its volume is not directly base area times h, which is quite intuitive as cone with same dimensions will have lesser volume. Its volume become 1/3rd of cylinders volume.

The volumes of a cone and a cylinder are related in the same way as the volumes of a pyramid and a prism are related. If the heights of a cone and a cylinder are equal, then the volume of the cylinder is three times as much as the volume of a cone.

The volume formula of a cone is V=13πr2h V = 1 3 π r 2 h V=\frac{1}{3} \pi r^2 h V=31​πr2h. Substitute the given values. We are given the volume and the radius, so we can substitute these into the formula.

This is due to the fact that the volume of a pyramidal object is always 1/3 that of its associated prismatic object (an object on the same base with the same height). So, the volume of a cone is 1/3 of that of its associated cylinder.

Thus, the volume of a cone is equal to one-third of the volume of a cylinder having the same base radius and height.

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