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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 Answer: The depth of the ice-cream is 11.11 cm.
