Question 971865
{{{r[co]}}}=radius of cone=7.5cm; {{{r[cy]}}}=radius of cylinder=5cm
{{{h[co]}}}=height of cone=12cm; {{{h[cy]}}}=height of liquid in cylinder
Volume of cone={{{(1/3)(pi)r[co]^2h[co]}}}
Volume in cylinder={{{(pi)r[cy]^2h[cy]}}}
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Since volume of the cone = volume in the cylinder:
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{{{(1/3)(pi)r[co]^2h[co]=(pi)r[cy]^2h[cy]}}} Divide each side by pi.
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{{{(1/3)r[co]^2h[co]=r[cy]^2h[cy]}}} Divide each side by {{{r[cy]^2}}}
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{{{r[co]^2h[co]/(3r[cy]^2)=h[cy]}}} Put in values.
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{{{((7.5cm)^2(12cm))/(3((5cm)^2))=h[cy]}}}
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{{{675cm^3/75cm^2=h[cy]}}}
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{{{9cm=h[cy]}}}
ANSWER: The height of the liquid in the cylinder would be 9 centimeters.