Sector $X$ has radius $5\text{ cm}$ and angle $2$ radians. Sector $Y$ has radius \(4\text{ c

Question

Sector $X$ has radius $5\text{ cm}$ and angle $2$ radians. Sector $Y$ has radius $4\text{ cm}$ and angle $3.5$ radians. Calculate the perimeter of each sector.[2] Calculate the area of each sector.[2] A student claims that sectors with equal perimeters must have equal areas. Use your results to explain whether the claim is correct.[1]

Accepted Answer

(a) Both $20\text{ cm}$. (b) $X:25\text{ cm}^2$; $Y:28\text{ cm}^2$. (c) The claim is false; these sectors are a counterexample.

Equal perimeters and unequal areas

Equal perimeters and unequal areas

Solution:

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