Two small pizzas with diameter 10 cost $15, while a large pizza with diameter of 16 cost $17 which pizza is less expensive per square inch

The larger pizza is less expensive per square inch

Step-by-step explanation:

we know that

The area of a circle (pizza) is equal to

step 1

Find the area of the smaller pizza

we have

----> the radius is half the diameter

substitute

Find the price per square unit

Remember that

The price of one smaller pizza is

so

step 2

Find the area of the larger pizza

we have

----> the radius is half the diameter

substitute

Find the price per square unit

so

Therefore

The larger pizza is less expensive per square inch

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!