A solid gold cube with edge of 2" is melted down and recast as a cone with a 3" radius base. Find the height of the cone.
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Given data:
Edge of the cube (a) = 2 inch
Radius of cone (r) = 3 inch
Solution:
Since the cube is melted and re-casted as cone, their volumes are equal.
Volume of cube = a^3
Volume of cone = 1/3 πr²h
= > 2 x 2 x 2 = (1/3) π x 3 x 3 x h
= > h = 8/ (3 x 3.14) inch
Height of the cone = 0.85 inch
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