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Thread starter 3 weeks ago
#1
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.
0
3 weeks ago
#2
(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 and ?
0
3 weeks ago
#3
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
Last edited by the bear; 3 weeks ago
0
Thread starter 3 weeks ago
#4
not sure
0
Thread starter 3 weeks ago
#5
(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
0
3 weeks ago
#6
(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
0
Thread starter 3 weeks ago
#7
(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)
0
3 weeks ago
#8
(Original post by naimaaaaaaaaa)
I get stuck after 2r = 3r(theta)
You can cancel out the since it's non-zero, and hence get what is.

Then sub it into the area equation and solve that for r.
1
Thread starter 3 weeks ago
#9
thankyou
0
Thread starter 3 weeks ago
#10
(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
1
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