Question

A gold ingot in the shape of a cylinder is melted and the resulting molten metal molded into a few identical conical ingots. If the height of each cone is half the height of the original cylinder and the area of the circular base of each cone is one fifth that of the circular base of the cylinder, then how many conical ingots can be made?

Accepted Answer

C. Volume of cylinder $V_{cyl} = A \cdot H$. Volume of cone $V_{cone} = \frac{1}{3} A_{cone} \cdot h_{cone} = \frac{1}{3} \left(\frac{A}{5}\right) \left(\frac{H}{2}\right) = \frac{A \cdot H}{30}$. Number of cones $n = \frac{V_{cyl}}{V_{cone}} = \frac{A \cdot H}{\frac{A \cdot H}{30}} = 30$.

Mensuration: Cylinder to Cones

Explanation

Practise this under exam conditions