Suppose a sphere, cylinder and cone all share the same radius. The cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder and cone?
1=cone = sphere - cylinder
2=24
3=50/3
4=36
5=24
i got answers you want
The volume formula for a sphere is given by $V_s=\frac{4}{3}\pi r^3$, where $r$ is the radius of the sphere. The volume formula for a cylinder is given by $V_c=\pi r^2h$, where $h$ is the height of the cylinder. The volume formula for a cone is given by $V_{cn}=\frac{1}{3}\pi r^2h$.
Since the cylinder and cone share the same height, we can write $V_c=\pi r^2h$ and $V_{cn}=\frac{1}{3}\pi r^2h$ as $V_c=3V_{cn}$.
Notice that the radius $r$ cancels out when comparing the volumes, so the relationship between the volume formulas for the sphere, cylinder, and cone is $\boxed{V_s=3V_c=9V_{cn}}$.