# The Third Dimension Exercises

### Example 1

Draw orthogonal drawings of the following solid from the top, front, left, and right viewpoints.

### Example 2

Draw the perspective view of the following solid given its orthogonal drawings.

### Example 3

Euler's formula says that the number of faces and the number of vertices in a polyhedron equal the number of edges plus 2. Use Euler's formula and see if it is true for these two solids. State why it does or does not apply to each solid.

### Example 4

Name and draw three kinds of solids that have 6 faces.

### Example 5

Draw a net for the following solid.

### Example 6

Identify the following solid and find the surface area using its net.

### Example 7

Identify the following solid and find the surface area using its net.

### Example 8

It's your little sister's birthday and you decide to buy her a cake. She still remembers how you massacred her Furby, so it'd better be a big cake. You decide to buy her this monstrous cake.

You want to cover the entire cake (even the bottom) with a layer of icing because, let's face it, icing is delicious. How much surface area do you have to cover with this icing (to the nearest square inch)?

### Example 9

She was really attached to that Furby, so you decide to buy her a present too. You chose a My Little Pony that fits in a cubic box that's 10 inches on each side. How many square inches of wrapping paper do you need to perfectly cover the gift box?