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anonymous
 one year ago
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?
anonymous
 one year ago
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

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mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Do you know the formula of the volume of a cone?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what are the choices?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0is there a fraction there? Is there an exponent there?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0A. V= 2/3 PIE R2 B. V= 4/3 PIE R3 C. V= 1/3 PIE R3 D. V= 1/3 PIE R2

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Do you mean this for the formula? \(\LARGE V_{cone} = \dfrac{\pi r^2 h}{3}\)

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Great. That is the correct formula. Notice the formula uses r to mean radius of the base, and h to mean the height of the cone.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Now let's look at your problem's cone. The radius is r. What is the diameter, d, compared to the radius?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0In any circle, what is the relationship between the diameter and the radius?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435165536451:dw

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0What is the diameter in terms of the radius?

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0@jazmine24 Do you understand that? d = 2r The diameter is twice the radius.

mathstudent55
 one year ago
Best ResponseYou've already chosen the best response.0Great. Now we need to find the height. We are told the height is twice the diameter. h = 2d, but we know d = 2r, so we have: h = 2(2r) h = 4r Now we have the radius is r, and the height is 4r. Now we can use the formula: \(\Large V_{cone} = \dfrac{\pi r^2 h}{3} \) \(\Large V_{cone} = \dfrac{\pi r^2 (4r)}{3} \) \(\Large V_{cone} = \dfrac{4 \pi r^3}{3} \)
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