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the volume of ice-cream in a cone is half the volume of the cone. the cone has a 3cm radius and 14cm height. what is the depth of the ice-cream correct to two decimal places?

V ( cone ) = 1/3 * 9 * 14 π = 42 π cm³
V ( ice-cream) = 42 π : 2 = 21 π cm³
1/3 r² π H = 21 π
r² H = 63
From the similarity of the triangles:
r : H = 3 : 14
14 r = 3 H
r = 3 H / 14
( 3 H/14) * H = 63
9 H³ / 196 = 63
H³ = 1,372
H ∛1,372
H = 11.11 cm
The depth of the ice-cream is 11.11 cm.  

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