Area of a circle

A circle has a radius of 10 cm. Find the area of the circle. Here's the circle, and here's the radius. 10 centimetres. Take pi as three point one four. How do you find the area of something round? Cut it up. Slice the circle into thin pieces, like a cake. Nothing has been thrown away. All the pieces are still here, so the area hasn't changed. Now arrange the pieces in a row, one pointing up, one pointing down. They lie down into a rectangle. Look at the bottom edge. It's made of the round edges of half the pieces, so it's half the rim, rolled out. The whole rim is pi diameters, so half of it is pi times the radius. And the height is one radius, because every slice is a radius long. A rectangle's area is length times breadth, so we can write it down. For this one, the length is the base and the breadth is the height. So the area is pi times the radius, times the radius. This circle's radius is 10, and the question says take pi as three point one four. So the area is three point one four, times 10, times 10. three hundred and fourteen square centimetres.

Your turn. A round tabletop has a diameter of 28 cm. Find the area of the tabletop. Take pi as 22 over 7. Take note. This one gives you the diameter. Try it first. Pause if you like. Same rule, and the same first line. The area is pi times the radius, times the radius. The rule uses the radius, and this question gives the diameter. So halve it first. 28 divided by 2 is 14 centimetres. Then 22 over 7, times 14, times 14. 14 divided by 7 is 2, so cross out the 7 and make the first 14 a 2. Then 22 times 2 times 14 is six hundred and sixteen square centimetres. An area is the circle, cut up and laid flat. Flat, it is a rectangle. One side is pi times the radius, and the other side is one radius. That's why the radius is in there twice. Never the diameter. Halve it first.