The volume of ice-cream in the cone is half the volume of the cone. The cone has a 3cm radius and 6cm height. What is the depth of the ice cream, correct to two decimal places?

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-measurements is in cm

1 Answer
Jan 28, 2018

h=4.76 cm

Explanation:

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V_"Cone"=piR^2H/3

R=3 cm

H=6

V_"Cone"=pi(3)^2(6/3)=18pi cm^3

V_"Ice Cream"=(18pi)/2=9pi cm^3

r is the radius of the Ice Cream.

h is the height (depth) of the Ice Cream.

The right triangles formed by the height of the cone and the two radii R and r are similar triangles by "AA" theorem. Therefore, the ratio of their corresponding sides are the same:

h/6=r/3

6r=3h

r=(3h)/6=h/2

V_"Ice Cream"=pir^2h/3

V_"Ice Cream"=pi(h/2)^2(h/3)

9pi=h^3/12pi

9=h^3/12

h^3=108

h=root(3)108=4.76 cm