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| Math Central | Quandaries & Queries |
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Question from charles, a student: A slice of pizza in the form of a sector of a circle has a perimeter of 24 inches. what value for the radius of the pizza makes the slice largest[when θ is the central angle in radians, the area of the sector is given by A= r^2 θ/2 and the length on the circle is given by s = rθ |
Hi Charles,
The perimeter of the pizza slice is composed of two straight pieces, each of length r inches, and an arc of the circle which you know has length s = rθ inches. Thus the perimeter has length
2r + rθ = 24 inches.
The area is given by
A= r2 θ/2
Solve the perimeter expression for θ and substitute into the area function. This gives the area as a function of r and you can now use the calculus you know to find the value of r that maximizes the area.
Harley
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