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A sector is cut from a circular sheet of radius 100 cm, the angle of the sector being 240c. if another circle of the area same as the sector is formed, then radius of the new circle is 81.65 cm.
A sector is cut from a circular sheet of radius 100 cm, the angle of the sector being 240c. if another circle of the area same as the sector is formed, then radius of the new circle is
The Correct answer is 81.65 cm
Calculate the area of the sector:
- The area of a whole circle is πr², where r is the radius. In this case, the radius is 100 cm, so the area of the whole circle is π * 100² = 10000π cm².
- The angle of the sector is 240°. Since a full circle has 360°, the ratio of the sector’s angle to the full circle’s angle represents the portion of the circle’s area it occupies. Therefore, the ratio is 240°/360° = 2/3.
- Multiply the whole circle’s area by this ratio to find the area of the sector: 10000π cm² * (2/3) = 6666.67π cm².
Relate the sector’s area to the new circle’s area:
We are given that the new circle has the same area as the sector. Therefore, the area of the new circle is also 6666.67π cm².
Find the radius of the new circle:
- The area of a circle is πr², where r is the radius. We know the area (6666.67π cm²) and need to solve for the radius (unknown).
- Rearrange the formula to isolate the radius: r = √(Area / π).
- Substitute the known area value: r = √(6666.67π cm² / π).
- Simplify: r = √(6666.67 cm²) ≈ 81.65 cm.
Therefore, the radius of the new circle is approximately 81.65 cm.
How to Calculate the Radius of the Circle?
1. Using the diameter:
- The diameter is the straight line that passes through the center of the circle and touches two opposite points on the circle’s circumference.
- The radius is always half the length of the diameter.
- Formula: radius = diameter / 2
2. Using the circumference:
- The circumference is the total length around the circle’s edge.
- The circumference is related to the radius by a constant value called pi (π), which is approximately equal to 3.14159.
- Formula: radius = circumference / (2π)
3. Using the area:
- The area of a circle is the space enclosed within the circle’s boundary.
- Formula: radius = √(area / π)
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Source: Math Hello Kitty
Categories: Math
