 You're at a pizza restaurant and order a 44 cm pepperoni pizza for $15.00. Twenty minutes later the waiter comes to your table and apologizes; apparently they have given your 44 cm pizza away to another customer. He says: "Would you like two 26 cm pizzas instead, for the same price? You get 8 more centimetres!". You would indeed get 8 more centimetres, and the person you're with is about to agree to the deal. Fortunately there was a math teacher at the table. He pointed out to the waiter that the 'deal' would be a ripoff ... and demanded three of the smaller pizzas. Was he right? The pictures below are to scale.
Of course he was! The 44 cm pizza, with radius 22 cm, has an area of πr2 = π(22)2 = 1521 cm2 One 26 cm pizza, with radius 13 cm, has an area of πr2 = π(13)2 = 531 cm2 Two of them have a total area of just 1062 cm2 This would be only about two thirds of the size of one large pizza. Asking for three pizzas, with a total area of 531 x 3 = 1593 cm2 would be much fairer! Once again a math teacher comes to the rescue! |
