A cube has 8 vertices, 12 edges, and 6 square faces. A soccer ball (also known as a buckyball or truncated icosahedron) has 12 pentagonal faces and 20 hexagonal faces. How many vertices and how many edges does a soccer ball have?

Question

A circular table is placed in a corner of a room so that it touches both walls. A mark is made on the edge of the table, exactly 18 inches from one wall and 25 inches from the other. What is the radius of the table?

I'd really appreciate if someone could explain them to me instead of just giving an answer. I'd like to learn how to do them.

Answer 1

F+V-E = 2
If you count all the vertices of each polygon, each vertex is counted twice. So,
12+20 + (5*12+6*20)/2 - E = 2
E = 120

draw a diagram. If you draw horizontal and vertical lines through the point and through the center of the circle, you will see that

(r-25)^2 + (r-18)^2 = r^2
so, r = 13 or 73
I guess only 73 fits the real world, eh?

Answer 2

Thank you Steve. That was very helpful. I was the only one in my class that got those right thanks to you! (And at my school, doing that actually gets you bragging rights.)

Answer 3

Nerd