Using Algebra to Determine Measurements from Volume and Percentages.

Theory:

The formula to find the volume of a container is usually length multiplied with the width multiplied by the height. Many children are used to this procedure to find the volume of a container, but when asked to give the dimensions from a given volume, many children don’t seem to know how to go about it. The way to solve this problem is by first introducing them to the change that the container is going through. If a change is given in the form of a fraction of percentage, the children should be taught to multiply that change to the dimension to find out the change in dimension.

A chocolate factory packages a certain amount of chocolates in a box with the following dimensions.

Height: 40 cm; Length: 20 cm; Width: 30 cm

After many years of using the same dimensions for the packaging, the factory decides to change the dimensions of the chocolate box. They want to increase the height of the box by 30 percent and reduce the width of the box in order to keep the same initial volume of the box.

1. What will be the new height and width of the box, if the length is kept the same?
2. If a piece of square chocolate has the dimensions, h = 12 cm, l = 10 cm, w = 10 cm; How many chocolates can be put into the box with the original dimensions?
3. How many chocolates can be put into the box with the new dimensions?

The following image is an image of the chocolate box.

Solution in Video format

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