Scale factor problem! "ET Pizza' produces two pizzas that are similar in shape...."

[tantrik]

Scale factor problem! "ET Pizza' produces two pizzas that are similar in shape...."

Dear friends,

I am unable to solve the following scale factor problem. Will appreciate your help here. Thanks in advance.

'ET Pizza' produces two pizzas that are similar in shape. The smaller pizza is 20 cm in diameter and costs $10. The larger pizza is 30 cm in diameter. What is a fair cost for the larger pizza?

The answer in the book is $33.75 but I am getting $15 (scale factor = 30/20=1.5; cost of larger pizza = $10*1.5 = $15). Let me know where I am mistaken.

 

[stapel]

I am unable to solve the following scale factor problem. Will appreciate your help here. Thanks in advance.

'ET Pizza' produces two pizzas that are similar in shape. The smaller pizza is 20 cm in diameter and costs $10. The larger pizza is 30 cm in diameter. What is a fair cost for the larger pizza?

The answer in the book is $33.75 but I am getting $15 (scale factor = 30/20=1.5; cost of larger pizza = $10*1.5 = $15). Let me know where I am mistaken.

The larger pizza has a diameter (and thus a radius) which is 1.5 times as large as that of the smaller pizza. But is the buyer buying just the diameter of the pizzas, or the entire area of the pizzas?

 

[Steven G]

You and the book are both wrong.

To start, you need to use the area, not the diameter.

area 20" pizza = pi r^2 = pi 10^2 = 314
area 30" pizza = pi r^2 = pi 15^2 = 707

If 314 costs $10, then 707 costs ?

Why not forget about the pi? Just because its a pizza pie doesn't mean we cant forget the pi!!

Divide pi 15^2 by pi 10^2 and get 15^2/10^2 = 225/100 = 2.25. So you are getting 2.25 times more for the larger pie. $10*2.25= $22.50. I feel that a fair price should be less than $22.50. You always get quantity discounts!

 

[tantrik]

Why not forget about the pi? Just because its a pizza pie doesn't mean we cant forget the pi!!

Divide pi 15^2 by pi 10^2 and get 15^2/10^2 = 225/100 = 2.25. So you are getting 2.25 times more for the larger pie. $10*2.25= $22.50. I feel that a fair price should be less than $22.50. You always get quantity discounts!

Thanks for the solution