Area left when a circle is cut from a square

A circle of radius 7 centimetres is cut out of a square piece of paper of side 14 centimetres. Here's the paper. A square, 14 centimetres on every side. And here's the circle. Radius 7. It just touches all four sides. Find the area of the paper that is left. Take pi as 22 over 7. Try it first. Pause if you like. Now cut it out. Out comes the circle. And that's the hole it leaves behind. One square piece of paper now becomes 2 pieces. The circle, and the paper around it. Now read the question again. It asks for the area of the paper that is left. That's this piece here, the one with the hole in it. Not the circle. The circle is the piece that came out. So what is left is the square minus the circle. That line goes down first, before any numbers. We look at the square first. The area of a square is length times breadth. Every side of a square is the same length. This side is 14, and this side is 14. So it's 14 times 14. That's one hundred and ninety six. Now the circle that came out. The area of a circle is pi r squared. That's pi, times r, times r. We're told to take pi as 22 over 7, and r is 7. 7 divided by 7 is 1, so cross out the 7 under the line and the first 7. That leaves 22 times 7. That's one hundred and fifty four. Now back to the first line that we wrote. Area of paper left is area of square, minus area of circle. One hundred and ninety six minus one hundred and fifty four. 42 square centimetres. And that is the paper that is left. If you got one hundred and fifty four, here's what happened. One hundred and fifty four is this piece here, the circle that came out. The paper that is leftover doesn't have the circle any more. When you cut a piece out from a paper, you have two pieces. When you put the circle back, it fits nicely back, and the square is a whole again. So the piece that is left is the whole, minus the piece that was cut out.