I got this question for homework and I'm not sure how to do it:
a) Find the ratio between the volume of a cone and the volume of a sphere.
b) Find the values of r and h if the ratio in a) = 1/3.
Thanks a lot.
I got this question for homework and I'm not sure how to do it:
a) Find the ratio between the volume of a cone and the volume of a sphere.
b) Find the values of r and h if the ratio in a) = 1/3.
Thanks a lot.
Volume of a cone is $\displaystyle \frac {1}{3}\pi r^2h$, Where r is the radius of the base and h is the height of the cone.
Volume of a sphere is $\displaystyle \frac {4}{3}\pi r^3$.
To find the ratio, divide the cone formula by the sphere formula:
$\displaystyle \frac {\frac {1}{3}\pi r^2h}{\frac {4}{3}\pi r^3}$
Factor out $\displaystyle \frac {1}{3}\pi r^2$ from the top and bottom:
$\displaystyle \frac {(\frac {1}{3}\pi r^2)(h)}{(\frac {1}{3}\pi r^2)(4r)}$
So your final answer is:
$\displaystyle \frac {h}{4r}$