Piling It On with a Conical Sand Pile

A cone has a circle for a base. The sides slant upward to meet at a single point called the vertex. The volume of a cone is one-third the volume of a cylinder that has the same base and same height. 

The volume of a circular cone is V = %r2h, where r is the radius of the cone 

The Problem What is the height of a cone if its diameter is twice the height and the volume of the cone is 12% cubic inches  

Use the formula for the volume of a cone, replacing the Pwith 12% and the height, h, with r. Why replace the height measure with r The diameter of a circle is twice the radius, so the diameter is equal to 2r. If the diameter is twice the height, then the diameter, 2r = 2h. The length of the radius is equal to the height. 

The radius is 6 inches. Because the radius and height are the same, the height is also 6 inches. 

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