anonymous
  • anonymous
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?
Geometry
katieb
  • katieb
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mathstudent55
  • mathstudent55
Do you know the formula of the volume of a cone?
anonymous
  • anonymous
what are the choices?
anonymous
  • anonymous
v = π r 2 h 3

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mathstudent55
  • mathstudent55
is there a fraction there? Is there an exponent there?
anonymous
  • anonymous
A. V= 2/3 PIE R2 B. V= 4/3 PIE R3 C. V= 1/3 PIE R3 D. V= 1/3 PIE R2
mathstudent55
  • mathstudent55
Do you mean this for the formula? \(\LARGE V_{cone} = \dfrac{\pi r^2 h}{3}\)
anonymous
  • anonymous
YEAH
mathstudent55
  • mathstudent55
Great. 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
  • mathstudent55
Now let's look at your problem's cone. The radius is r. What is the diameter, d, compared to the radius?
mathstudent55
  • mathstudent55
In any circle, what is the relationship between the diameter and the radius?
mathstudent55
  • mathstudent55
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mathstudent55
  • mathstudent55
What is the diameter in terms of the radius?
anonymous
  • anonymous
D=2r
mathstudent55
  • mathstudent55
@jazmine24 Do you understand that? d = 2r The diameter is twice the radius.
anonymous
  • anonymous
yes i do understand
mathstudent55
  • mathstudent55
Great. 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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