help!?! The radius of a sphere and of a cylinder are the same. The diameter of the sphere and the height of the

Question

whpalmer4 · Answer

$$V_{sphere} = \frac{4}{3}\pi r^3$$$$V_{cone} = \frac{1}{3}\pi r^2 h$$We know in this case that the height of the cone, $h$ is the radius $r$ so that becomes
$$V_{cone} = \frac{1}{3}\pi r^3$$
With that in mind, what's your answer?

whpalmer4 · Answer

Oh, and the volume of the cylinder:
$$V_{cylinder} = \pi r^2h = 2\pi r^3$$because the height $h = 2r$

anonymous · Answer

B?

whpalmer4 · Answer

$$\frac{4}{3}\pi r^3 = 2\pi r^3 - 2(\frac{1}{3}\pi r^3)$$We can see that $\pi r^3$ is a common factor to all of that, leaving us with $$\frac{4}{3} = 2 - \frac{2}{3}$$if we convert the 2 to 6/3, we see that the equation is correct, so answer B is correct.  Good job!

anonymous · Answer

Thank you :)

whpalmer4 · Answer

Hopefully you know those formulas well enough to recall them from memory.  I'll confess I had to look up the formula for the cone :-)

anonymous · Answer

hopefully! lol