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

`r(v)=\sqrt{(3v)/(20\pi ) }` inches

Explanation:

Volume of the cone v =
`(1)/(3)\pi r^(2) h` cubic inches.

Conical artifact is 20 inches tall.

So, h = 20

Now,

`(1)/(3)\pi r^(2) h` = v

`(1)/(3)\pi r^(2)(20)=v`

`r^(2)=(3v)/(20\pi )`

`r(v)=\sqrt{(3v)/(20\pi ) }` inches