The Sweet Surprises Candy Factory specializes in custom-molded chocolate candies. The factory supervisor purchases chocolate in bars that are shaped like rectangular prisms, which are then sliced and melted according to which types of candies need to be made.

The dimensions of the original chocolate bars are shown.

First, we need to determine the volume of chocolate, in cubic inches, contained in one chocolate bar.

In the figure below, drag the dimensions from the prism onto the appropriate place in the formula to calculate the volume of the chocolate bar.

Now that you have correctly identified the dimensions, calculate the volume of the chocolate bar.

Check Your Answer

282 1 over 32 1 32 in. ³

For one recipe, the chef needs 180 1 over 2 1 2 cubic inches of chocolate. To obtain this amount of chocolate, the chef will slice a chocolate bar as shown in the diagram.

What will be the resulting length of the chocolate bar that the chef will melt to use for his recipe?

Interactive popup. Assistance may be required. Hint Think of the base of the prism as the square on the right-hand face so that the prism is lying on its side. By doing this, you can calculate the area of the base, and then divide it into the volume needed for the recipe. This process will determine the height of the prism. Interactive popup. Assistance may be required.

Check Your Answer

Volumes of Pyramids

A customer has ordered chocolate candies that are solid and in the shape of square pyramids. The dimensions in the schematic are shown in the figure below.

In the figure below, drag the dimensions from the pyramid onto the appropriate place in the formula to calculate the volume of the candies.

Now that you have correctly identified the dimensions, calculate the volume of one of the pyramid-shaped chocolate candies.

Check Your Answer

9 over 16 9 16 in. ³

Bonus Question:
How many of the pyramid-shaped candies could be made from one full-sized chocolate bar?

Interactive popup. Assistance may be required. Hint Divide the volume of one candy into the volume of one full chocolate bar, which you calculated earlier. Think about how you will handle any remainder. Interactive popup. Assistance may be required.

Check Your Answer

501 candies (The remainder will be discarded or used for a different project.)

Practice

1. A vase is in the shape of a rectangular prism and has the dimensions shown below.

   

   If the vase is filled with water to a height of 18 cm, what is the volume of water inside the vase? Use the grid below to record your answer. Type your answer in the boxes in front of and behind the decimal. Click inside each box to enter the numeral that belongs in the box, and then click the bubble beneath the number to shade the bubble that matches the numeral. Incorrect portions of your answer will be shaded gray.

2. A tent is shaped like an isosceles triangular prism.
   

   Calculate the volume of air that will be contained inside the tent.

   Interactive popup. Assistance may be required. Hint Use the formula V = Bh, where B represents the area of one triangular base. Interactive popup. Assistance may be required.

   Check Your Answer

   V = 1 over 2 1 2 (6 ft)(41 over 2 1 2 ft)(10 ft) = 135 ft³
3. A metronome is made from wood and is shaped like a square pyramid with the dimensions shown.
   

   Calculate the volume of wood required to construct the metronome.

   Hint Use the formula, V = 1 over 3 1 3 Bh, where B represents the area of the triangular base. Interactive popup. Assistance may be required.

   Check Your Answer

   V = 1 over 3 1 3 (51 over 2 1 2 in. × 51 over 2 1 2 in.)(9 in.) = 903 over 4 3 4 in.³