gaiamiah
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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?

Respuesta :

kyletubehdtv
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
JannetPalos

Answer:

[tex]r(v)=\sqrt{\frac{3v}{20\pi } }[/tex] inches

Step-by-step explanation:

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

Conical artifact is 20 inches tall.

So, h = 20

Now,

[tex]\frac{1}{3}\pi r^{2} h[/tex] = v

[tex]\frac{1}{3}\pi r^{2}(20)=v[/tex]

[tex]r^{2}=\frac{3v}{20\pi }[/tex]

[tex]r(v)=\sqrt{\frac{3v}{20\pi } }[/tex] inches

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