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=(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=(4)/(3)*(22)/(7)*(1.4)^3 \\ =(88*2.744)/(21) \\ =(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*11.4987 \\ =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*0.06 \\ =0.90379782\text{ dollars} \end{gathered}`

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

`0.90379782*130=117.4937166\text{ dollars}`

Thus, the answer is $117.49.