## 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?

1. mathstudent55

Do you know the formula of the volume of a cone?

2. anonymous

what are the choices?

3. anonymous

v = π r 2 h 3

4. mathstudent55

is there a fraction there? Is there an exponent there?

5. 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

6. mathstudent55

Do you mean this for the formula? $$\LARGE V_{cone} = \dfrac{\pi r^2 h}{3}$$

7. anonymous

YEAH

8. 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.

9. mathstudent55

Now let's look at your problem's cone. The radius is r. What is the diameter, d, compared to the radius?

10. mathstudent55

In any circle, what is the relationship between the diameter and the radius?

11. mathstudent55

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12. mathstudent55

What is the diameter in terms of the radius?

13. anonymous

D=2r

14. mathstudent55

@jazmine24 Do you understand that? d = 2r The diameter is twice the radius.

15. anonymous

yes i do understand

16. 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: $$\Large V_{cone} = \dfrac{\pi r^2 h}{3}$$ $$\Large V_{cone} = \dfrac{\pi r^2 (4r)}{3}$$ $$\Large V_{cone} = \dfrac{4 \pi r^3}{3}$$