naimaaaaaaaaa
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Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm^2. Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.
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RDKGames
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(Original post by naimaaaaaaaaa)
Figure 1 shows a sector AOB of a circle with centre O and radius r cm. The angle AOB is θ radians. The area of the sector AOB is 11 cm^2. Given that the perimeter of the sector is 4 times the length of the arc AB, find the exact value of r.
What is the length of the arc AB in terms of r and \theta ?
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the bear
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so the perimeter is made up of 2 radii and the curved bit....

P = 2r + rθ

we know that P = 4x rθ

and that the area A = 0.5 r2 x θ

so 0.5 r2 x θ = 11

now you can find r and θ
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naimaaaaaaaaa
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(Original post by RDKGames)
What is the length of the arc AB in terms of r and \theta ?
not sure
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naimaaaaaaaaa
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(Original post by the bear)
so the perimeter is made up of 2 radii and the curved bit....

P = 2r + rθ

we know that P = 4x rθ

and that the area A = r2 x θ

so r2 x θ = 11

now you can find r and θ
I don't get how
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the bear
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(Original post by naimaaaaaaaaa)
I don't get how
we know that

2r + rθ = 4rθ

because the perimeter ( LHS ) is 4 times the arc length ( RHS )

by rearranging it you can find θ

and we know that

0.5 r2θ = 11

you can then put in the value of θ and find r
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naimaaaaaaaaa
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(Original post by the bear)
we know that

2r + rθ = 4rθ

because the perimeter ( LHS ) is 4 times the arc length ( RHS )

by rearranging it you can find θ

and we know that

0.5 r2θ = 11

you can then put in the value of θ and find r
I get stuck after 2r = 3r(theta)
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RDKGames
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(Original post by naimaaaaaaaaa)
I get stuck after 2r = 3r(theta)
You can cancel out the r since it's non-zero, and hence get what \theta is.

Then sub it into the area equation and solve that for r.
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naimaaaaaaaaa
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(Original post by RDKGames)
You can cancel out the r since it's non-zero, and hence get what \theta is.

Then sub it into the area equation and solve that for r.
thankyou
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naimaaaaaaaaa
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(Original post by the bear)
we know that

2r + rθ = 4rθ

because the perimeter ( LHS ) is 4 times the arc length ( RHS )

by rearranging it you can find θ

and we know that

0.5 r2θ = 11

you can then put in the value of θ and find r
thankyou
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