Equations and inequalities

Question

A pizzeria is putting on a pie-by-length event where customers may order a rectangular pizza that is 6” wide by the length of their choice. Customers may also order circle pizzas of several diameters

a~~Solving the equation 6L=pie(L/2)^2 will give the length/diameter where the two shapes have the same area. how was this formula was made

b~~what length/diameter will the two shapes of pizza have the same area.., and Round the answer to the nearest tenth of an inch

c~~The pizzeria owner says when customers order pie-by-length they feel they are getting more for less. How could he justify this

Answer 1

A. The area of a circle is pi(r)². The diameter is twice the radius, so if we are given a diameter equal to the length of the rectangular pizza), we have to half it to get the radius.

 

The area of a rectangle is L X W. We are given that the width is 6", so the area is 6L.

 

If the two areas are equal, we get 6L = pi(L/2)²

 

B. 6L = pi(L/2)² = piL²/4

6 = piL/4

24 = piL

L = 24/pi

L = 7.6

 

C. Think about it. I can order a circular pizza that is 7.6" across, or I can order a 7.6" x 6" pizza, which is going to look larger. Technically, by rounding to the tenth, the rectangular pizza has a slightly higher area, but by about 1/4-inch.