The Dollhouse Pizza Parlor sells two sizes of pizza: small-sized and doll-sized. All of their pizzas are shaped like regular octagons. If the length of the crust of each slice is 3 inches for a small slice and 1 inch for a doll slice, how many times larger is the area of a small pizza compared to a doll pizza?
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I have compared the area of both the sectors as it is directly proportional to the area of whole octagon.
Radius of small sector and doll sector is π 1 2 and π 4 respectively. [ If in a circle of radius r , an arc of length l subtends an angle θ radian at the centre , then we have r = θ l ]
Area of small sector = 8 π ⋅ ( π 1 2 ) 2 = π 1 8
Area of doll sector = 8 π ⋅ ( π 4 ) 2 = π 2
⇒ Area of doll vector Area of small vector = 1 9