The original question includes a diagram: Two similar circular sectors side by side, the smaller with radius r and arc length 6, the larger with radius r + 3.
Two sectors of circles are similar. The smaller has radius r and the larger has radius r + 3.
The arc length of the smaller sector is 6. The difference between the areas of the sectors is 21.
Find the positive difference between the perimeters of the sectors.
- A4.5
- B7
- C8
- D9
- E10.5
- F14
- G15
Show the answer and worked solution
answer · C
- A4.5
- B7
- C8
- D9
- E10.5
- F14
- G15
Similar sectors share an angle θ, and the smaller arc gives rθ = 6. The areas are 12 r2θ and 12 (r+3)2θ, so their difference is 12θ(6r + 9) = 3r(6r+9) = 18 + 27r. Setting that equal to 21 gives r = 9, so θ = 23. The perimeters are 2(9) + 6 = 24 and 2(12) + 12⋅23 = 32, differing by 8.