A solid shape is made of identical cubes. The side elevation, plan view, and front elevation are shown. How many cubes were used to make this shape?
Plans and elevations are ways of representing a three-dimensional shape in two dimensions. The view from the top or above the shape is the plan. The views from the front and side are called the front elevation and side elevation. We have been given the three views. So how do we work out how many cubes were used to make the shape? Well we need to try and picture what this shape would look like in three dimensions.
Let’s begin with the side elevation. We can see that this is in the shape of a cross. Let’s assume that the side of the shape is a cross made out of five blocks. That would look something like this. The plan and front elevations are solid rectangles. So this actually tells us that the cross pattern must continue through the three-dimensional shape with no indents.
Here is the first two rows. In fact, the shape is a prism, and it has a constant cross section of a cross. The cross-section is made up of five squares. Each row in fact is made up of five cubes. The plan view and the front elevation tell us that there must be four of these rows. That’s four rows of five cubes. four multiplied by five is 20. That means there must be 20 cubes in this shape.