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Jackson buys a grape snow cone on a hot day. By the time he eats all the "snow" off the top, the paper cone is filled with 27 pi cm^3 cubed of melted purple liquid. The radius of the cone is 3 cm.

What is the height of the cone?
Either enter an exact answer in terms of pi or use 3.14 for pi.

Sagot :

rococo908

Answer:

9 cm

Step-by-step explanation:

Use the cone volume formula, V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

Plug in the volume and radius, and solve for h, the height:

V = [tex]\pi[/tex]r²[tex]\frac{h}{3}[/tex]

27[tex]\pi[/tex] = [tex]\pi[/tex](3²)[tex]\frac{h}{3}[/tex]

27[tex]\pi \\[/tex] = 9[tex]\pi[/tex][tex]\frac{h}{3}[/tex]

3 = [tex]\frac{h}{3}[/tex]

9 = h

So, the height of the cone is 9 cm

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