Varying the Unit
In this lesson, we study how changing the shape of an object while keeping the same volume affects the surface area of the object. We begin by seeing how many different retangular solids can be built using a certain number of cubes, say 12. Here are several different solids with a volume of 12 cubic units (a single cube will represent the cubic unit - see Surface Area and Volume)
What are the surface areas of the various rectangular solids? Remember that one face of the unit cube is a square unit, the unit of area measure. What is the effect on the surface area of changing the shape of the solid? Why do you think the surface area is affected that way?
Now, let's change the measurement units. What are the dimensions, surface area, and volume of the solids above if the following measures are used?
Becoming familiar with measurement of dimension, surface area and volume are fundamental concepts in geometry. By exploring the effects of changing units as well as shape, students develop important ideas about finding surface areas and volumes of various two- and three-dimensional geometric shapes. Discuss with your child situations involving measurement that crop up around home and in the yard. It will help them see the importance of these concepts.