Final answer:
To find the length of an arc with a central angle of 90° and a radius of 7 cm, use the arc length formula s = (θ/360) × 2πr, which yields an approximate length of 11 cm for θ = 90°.
Step-by-step explanation:
To solve for the length of an arc ABC with a central angle of 0-90° and a radius of 7 cm, we can use the formula for arc length, which is a fraction of the circumference of the entire circle. The formula is:
arc length (s) = (θ/360) × 2πr
where θ is the angle in degrees and r is the radius of the circle. For this example:
• θ is within 0-90° (let's assume θ is 90° for calculation purposes).
• r is 7 cm.
Therefore, the arc length s would be:
s = (90/360) × 2π × 7
s = (1/4) × 2π × 7
s = ½π × 7
s = 3.5π cm
Since π is approximately 3.1416, the approximate arc length s is:
s = 3.5 × 3.1416
s ≈ 11 cm
This is the arc length for an arc of 90 degrees and a radius of 7 cm.