Draw orthogonal drawings of the following solid from the top, front, left, and right viewpoints.
Hint
The shaded part indicates the front.
Answer
Example 2
Draw the perspective view of the following solid given its orthogonal drawings.
Hint
The left view blocks some of the squares from being seen.
Answer
Example 3
Euler's formula says that the number of faces plus the number of vertices in a polyhedron equal the number of edges plus 2. Use Euler's formula and see if it's true for these two solids. State why it does or does not apply to each solid.
Hint
Euler's formula is F + V = E + 2 for polyhedrons.
Answer
Euler's formula applies to the pentagonal pyramid, since 6 + 6 = 10 + 2 = 12. Euler's formula does not apply to the cone because it's not a polyhedron.
Example 4
Name and draw three kinds of solids that have 6 faces.
Hint
There are actually four possible answers, so you've got options. Two of them are prisms, one is a pyramid, and the other is a generic polyhedron sometimes in the shape of a "bipyramid."
Answer
Cube, rectangular prism, pentagonal pyramid, or hexahedron.
Example 5
Draw a net for the following solid.
Hint
Imagine cracking it open from the top vertex and letting the faces fall to the sides of the base.
Answer
Example 6
Identify the following solid and find the surface area using its net.
Hint
The surface area is equal to the sum of the area of each polygon.
Answer
The surface area of the triangular prism is 156 in2.
Example 7
Identify the following solid and find the surface area using its net.
Hint
Draw the net by "unwrapping" the solid. The shape has six faces, so there should be six polygons.
Answer
The solid is a rectangular prism with surface area 378 units2.
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)?
Hint
The net for the solid looks like this:
The long side of the rectangle goes around the circles perfectly, so its length is the circumference of the circle (2πr).
Answer
You need to cover 1680π ≈ 5278 square inches of cake with icing. Bring on the sugar high.
Example 9
Your sister 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?
Hint
Draw the net. All the edges of a cube are the same length.
Answer
You'll need 600 square inches of wrapping paper. The things you go through for your sister.
