Answer:
The angle the wire now subtends at the center of the new circle is approximately 145.7°
Step-by-step explanation:
The radius of the arc formed by the piece of wire = 15 cm
The angle subtended at the center of the circle by the arc, θ = 68°
The radius of the circle to which the piece of wire is reshaped to = 7 cm
Let 'L' represent the length of the wire
By proportionality, we have;
L = (θ/360) × 2 × π × r
L = (68/360) × 2 × π × 15 cm = π × 17/3 = (17/3)·π cm
Similarly, when the wire is reshaped to form an arc of the circle with a radius of 7 cm, we have;
L = (θ₂/360) × 2 × π × r₂
∴ θ₂ = L × 360/(2 × π × r₂)
Where;
θ₂ = The angle the wire now subtends at the center of the new circle with radius r₂ = 7 cm
π = 22/7
Which gives;
θ₂ = (17/3 cm) × (22/7) × 360/(2 × (22/7) × 7 cm) ≈ 145.7°.
