Question

4). A piece of wire in the shape of an arc of a circle

Answer 1

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°.