You stop at a pizza shop where each pizza is cut into 8 slic

You stop at a pizza shop where each pizza is cut into 8 slices. Would you be more filled by eating one slice from a pizza with a 16 inch diameter or two slices from a pizza with a 12 inch diameter? In other words, use the area of a sector formula to determine which has larger area?

Solution

Area of sector A = (/360) r²

Pizza is sliced inti 8 pieces

==> Angle = 360/8 = 45^o

==> Area of sector = (45/360) r²

==> A = (1/8) r²

Now 16 inch diameter ==> radius = 8 inches

Area A₁ = (1/8) (8)² = 8 square units

12 inch diameter ==> radius = 6 inches

Area A₂ = (1/8) (6)² = 9/2 square units

A₁ > A₂

Hence Pizza slice with 16inches diameter fills more than the slice with 12inches diameter.