Question

10.

a.
A piece of wire, 10 cm long, is formed into the shape of a sector of a circ
of radius k cm and angle x radians.
10
i.
Show that x =
2
k
Find an expression for the area of the sector.
ii.

Answer 1

To find the angle x, set up a proportion using the arc length formula. The area of the sector is 5k.

Step-by-step explanation:

To find the value of x, we can set up a proportion using the arc length formula. The arc length of a sector is given by L = rθ, where L is the arc length, r is the radius, and θ is the angle in radians.

Given that the wire is formed into the shape of a sector, L = 10 cm (length of the wire) and r = k cm (radius of the sector). We can set up the proportion: 10 = kx. Solving for x, we get x = 10 / k.

To find the area of the sector, we use the equation for the area of a sector: A = 1/2 r^2 θ. Substituting the values, A = 1/2 k^2 (10 / k) = 5k.

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