Question

A chocolatier makes chocolate bon-bons in the shape of a sphere with a diameter of 2.8 cm. The chocolate used in the bon-bons has a density of 1.31 g/cm^3. If the chocolate used costs $0.06 per gram, how much would the chocolate for 130 bon-bons cost, to the nearest cent?

Answer 1

Given:

The diameter of the chocolate bonbons is 2.8 cm.

To find:

The cost of 130 bonbons.

Solution:

It is known that the volume of the sphere is given by:

$V=\frac{4}{3}\pi r^3$

Here, the radius of the sphere is 1.4 cm.

So, the volume of the given sphere is:

$\begin{gathered} V=\frac{4}{3}\times\frac{22}{7}\times(1.4)^3 \\ =\frac{88\times2.744}{21} \\ =\frac{241.472}{21} \\ =11.4987cm^3 \end{gathered}$

Now, the density of the chocolate bon-bon is 1.31 g/cm^3. So, the weight of the chocolate bon-bon is:

$\begin{gathered} \text{Density}=1.31\times11.4987 \\ =15.063297\text{ grams} \end{gathered}$

Now, the cost of chocolate is $ 0.06 per gram. So, the cost is:

$\begin{gathered} \text{ cost}=15.063297\times0.06 \\ =0.90379782\text{ dollars} \end{gathered}$

So, the cost of 130 chocolate bon-bons is:

$0.90379782\times130=117.4937166\text{ dollars}$

Thus, the answer is $117.49.