Question 1206937: The volume of a right circular cone is 5 litres. Calculate the volumes of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base. Give your answers to the nearest ml.
Answer by greenestamps(13198)   (Show Source):
You can put this solution on YOUR website!
The two parts into which the original cone is divided are a small cone similar to the original cone and the frustum that is left.
According to the given information, the height of the small cone is 1/3 of the height of the original cone. By a powerful general principle regarding similar figures, the volume of the small cone is (1/3)^3 = 1/27 of the volume of the original cone.
The volume of the original cone is 5 liters = 5000ml. 1/27 of that volume, rounded to the nearest ml, is 185ml.
So the volume of the small cone is 185ml, and the volume of the frustum is 5000-185 = 4815ml.
ANSWERS: 185ml and 4815ml
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