Question

which of the following functions gives the radius,r(v), of a conical artifact that is 20 inches tall as a function of its volume,v, in cubic inches?

Answer 1

V=(pi)r2h and we know that h = 2r   so we can replace h with 2r and we get  V = (pi)r2(2r) V=2(pi)r3    Hope this helps

Answer 2

Answer:

$r(v)=\sqrt{\frac{3v}{20\pi } }$ inches

Step-by-step explanation:

Volume of the cone v = $\frac{1}{3}\pi r^{2} h$ cubic inches.

Conical artifact is 20 inches tall.

So, h = 20

Now,

$\frac{1}{3}\pi r^{2} h$ = v

$\frac{1}{3}\pi r^{2}(20)=v$

$r^{2}=\frac{3v}{20\pi }$

$r(v)=\sqrt{\frac{3v}{20\pi } }$ inches