问题1.用π求出在4 cm半径的圆的中心处与30 o角对向的弧的长度。
解决方案：
Given,
Radius = 4 cm
Angle subtended at the centre = 30°
Length of arc = θ/360 × 2πr
Length of arc = 30/360 × 2π × 4 cm
= 2π/3
Therefore, the length of arc that subtends an angle of 30o degree is 2π/3 cm
问题2.找到半径为5 cm的圆的中心与长度为5π / 3 cm的弧相对的角度。
解决方案：
Length of arc = 5π/3 cm
Length of arc = θ/360 × 2πr cm
5π/3 cm = θ/360 × 2πr cm
θ = 60°
Therefore, the angle subtended at the centre of circle is 60°
问题3.长度为20πcm的弧在圆心处与144°角对向。找到圆的半径。
解决方案：
Length of arc = 20π cm
θ = Angle subtended at the centre of circle = 144°
Length of arc = θ/360 × 2πr cm
θ/360 × 2πr cm = 144/360 × 2πr cm = 4π/5 × r cm
20π cm = 4π/5 × r cm
r = 25 cm.
Therefore, the radius of the circle is 25 cm.
问题4.长度为15厘米的弧在圆心处与45°角对向。用π表示圆的半径。
解决方案：
Length of arc = 15 cm
θ = Angle subtended at the centre of circle = 45°
Length of arc = θ/360 × 2πr cm
= 45/360 × 2πr cm
15 cm = 45/360 × 2π × r cm
15 = πr/4
Radius = 15×4/ π = 60/π
Therefore, the radius of the circle is 60/π cm.
问题5.找到半径为“ a” cm的圆的中心与长度为( ππ / 4)cm的弧对向的角度。
解决方案：
Radius = a cm
Length of arc = aπ/4 cm
θ = angle subtended at the centre of circle
Length of arc = θ/360 × 2πr cm
θ/360 × 2πa cm = aπ/4 cm
θ = 360/ (2 x 4)
θ = 45°
Therefore, the angle subtended at the centre of circle is 45°
问题6：半径为4 cm的圆的扇形对角为30°。找到该领域的领域。
解决方案：
Radius = 4 cm
Angle subtended at the centre O = 30°
Area of the sector = θ/360 × πr2
= 30/360 × π42
= 1/12 × π16
= 4π/3 cm2
= 4.19 cm2
Therefore, the area of the sector of the circle = 4.19 cm2
问题7.半径为8 cm的圆的扇形包含135 o的角。查找部门领域。
解决方案：
Radius = 8 cm
Angle subtended at the centre O = 135°
Area of the sector = θ/360 × πr2
Area of the sector = 135/360 × π82
= 24π cm2
= 75.42 cm2
Therefore, area of the sector calculated = 75.42 cm2
问题8.半径为2 cm的圆的扇形区域的面积为πcm 2 。找到扇形所包含的角度。
解决方案：
Radius = 2 cm
Area of sector of circle = π cm2
Area of the sector = θ/360 × πr2
= θ/360 × π22
= πθ/90
π = π θ/90
θ = 90°
Therefore, the angle subtended at the centre of circle is 90°
问题9.半径为5 cm的圆的扇形区域的面积为5πcm 2 。找到扇形所包含的角度。
解决方案：
Radius = 5 cm
Area of sector of circle = 5π cm2
Area of the sector = θ/360 × πr2
= θ/360 × π52
= 5πθ/72
5π = 5πθ/72
θ = 72°
Therefore, the angle subtended at the centre of circle is 72°
问题10.如果相应的弧长为3.5 cm，则找到半径为5 cm的圆的扇形区域。
解决方案：
Radius = 5 cm
Length of arc = 3.5 cm
Length of arc = θ/360 × 2πr cm
= θ/360 × 2π(5)
3.5 = θ/360 × 2π(5)
3.5 = 10π × θ/360
θ = 360 x 3.5/ (10π)
θ = 126/ π
Area of the sector = θ/360 × πr2
= (126/ π)/ 360 × π(5)2
= 126 x 25 / 360
= 8.75
Therefore, the area of the sector = 8.75 cm2
问题11：在半径为35 cm的圆中，圆弧在中心处对角为72°。找到圆弧的长度和扇形的面积。
解决方案：
Radius = 35 cm
Angle subtended at the centre = 72°
Length of arc = θ/360 × 2πr cm
= 72/360 × 2π(35)
= 14π
= 14(22/7)
= 44 cm
Area of the sector = θ/360 × πr2
= 72/360 × π 352
= (0.2) x (22/7) x 35 × 35
= 0.2 × 22 × 5 × 35
Area of the sector = (35 × 22) = 770 cm2
Length of arc = 44cm
问题12.半径为5.7 m的圆的扇形的周长为27.2 m。找到该领域的领域。
解决方案：
Perimeter of sector includes length of arc and two radii
Radius = 5.7 cm = OA = OB
Perimeter of the sector = 27.2 m
Length of arc = θ/360 × 2πr m
Perimeter = l + 2r
Perimeter of the sector = θ/360 × 2πr + OA + OB
27.2 = θ/360 × 2π x 5.7 cm + 5.7 + 5.7
27.2 – 11.4 = θ/360 × 2π x 5.7
15.8 = θ/360 × 2π x 5.7
θ = 158.8°
Area of the sector = θ/360 × πr2
Area of the sector = 158.8/360 × π 5.72
Area of the sector = 45.03 m2
问题13：半径圆的某个扇区的周长是5.6 m和27.2 m。找到该领域的领域。
解决方案：
Radius of the circle = 5.6 m = OA = OB
Perimeter of the sector = Perimeter = l + 2r = 27.2
Length of arc = θ/360 × 2πr cm
θ/360 × 2πr cm + OA + OB = 27.2 m
θ/360 × 2πr cm + 5.6 + 5.6 = 27.2 m
θ = 163.64°
Area of the sector = θ/360 × πr2
Area of the sector = 163.64/360 × π 5.62
= 44.8
Therefore, the area of the sector = 44.8 m2