Two chocolate fountains are mathematically similar. The bowl of the smaller fountain has a curved surface area of 942 centimeters
squared. It holds 1.2 kilograms of melted chocolate. The bowl of the larger fountain has a curved surface area of 2119.5 centimeters
squared. Paula bought the larger fountain and wants to buy enough chocolate to fill it. Chocolate is sold in 200-gram bars. How many of these bars does she need to buy?
In order to solve this problem, we need to consider our length, area, and volume
scale factors, as the two fountains are mathematically similar. In order to go from an area scale factor to a length scale factor, we
square-root. And to go from a length scale factor to a volume scale factor, we need to cube this
In our question, we’re told the curved surface area of both of the bowls. This means that our area scale factor can be calculated by dividing 2119.5 by
942. This is equal to 2.25. Therefore, our ASF is equal to 2.25. Square-rooting this answer will give us our length scale factor, or LSF. The square root of 2.25 is 1.5. Cubing this value of 1.5 will give us our volume scale factor. 1.5 cubed is equal to 3.375. Therefore, the volume scale factor is 3.375.
We’re told in the question that the smaller fountain holds 1.2 kilograms of melted
chocolate. Therefore, it is the volume scale factor that we are going to use. To calculate the amount of chocolate that the larger fountain can hold, we need to
multiply 1.2 by the volume scale factor. In this case, multiply 1.2 by 3.375. This gives us 4.05. Therefore, the larger fountain holds 4.05 kilograms.
One kilogram is the same as 1000 grams. Therefore, 4.05 kilograms is equal to 4050 grams. We’re told in the question that chocolate is sold in 200-gram bars. We therefore need to divide 4050 by 200. Dividing 4050 by 200 gives us 20.25. 20 bars of chocolate would only buy 4000 grams, or four kilograms. Therefore, we need to round this answer up, and Paula needs to buy 21 bars. This will ensure that she has enough chocolate to fill the larger fountain.