The area of a segment of a circle can be calculated using the formula:

Area = 0.5 * r² * (θ - sinθ)

where r is the radius of the circle, and θ is the angle subtended at the center of the circle in radians.

Given that the area of the segment is 15 m² and the angle subtended at the center is 65°, we can substitute these values into the formula and solve for r.

First, we need to convert the angle from degrees to radians. We know that π radians = 180°, so 65° = 65 * π / 180 = 1.134 radians.

Substituting the given values into the formula, we get:

15 = 0.5 * r² * (1.134 - sin(1.134))

Solving this equation for r, we get:

r² = 15 / (0.5 * (1.134 - sin(1.134)))

r = sqrt(15 / (0.5 * (1.134 - sin(1.134))))

Using a calculator, we find that r ≈ 6.4 m.

So, the radius of the circle is approximately 6.4 m, correct to one decimal place.

Question

The area of a segment of a circle can be calculated using the formula:

Area = 0.5 * r² * (θ - sinθ)

where r is the radius of the circle, and θ is the angle subtended at the center of the circle in radians.

Given that the area of the segment is 15 m² and the angle subtended at the center is 65°, we can substitute these values into the formula and solve for r.

First, we need to convert the angle from degrees to radians. We know that π radians = 180°, so 65° = 65 * π / 180 = 1.134 radians.

Substituting the given values into the formula, we get:

15 = 0.5 * r² * (1.134 - sin(1.134))

Solving this equation for r, we get:

r² = 15 / (0.5 * (1.134 - sin(1.134)))

r = sqrt(15 / (0.5 * (1.134 - sin(1.134))))

Using a calculator, we find that r ≈ 6.4 m.

So, the radius of the circle is approximately 6.4 m, correct to one decimal place.

Knowee AI · Accepted Answer