问题1.找到半径为4.2厘米的圆的周长和面积。
解决方案：
Radius = 4.2 cm
Circumference of a circle = 2πr
= 2 × (22/7) × 4.2
= 26.4 cm
Area of a circle = πr2
= (22/7) x 4.22
= (22/7) × 4.2 × 4.2
= 55.44 cm2
Therefore, circumference = 26.4 cm and area of the circle = 55.44 cm2
问题2.找到面积为301.84 cm 2的圆的周长。
解决方案：
Area of circle = 301.84 cm2
Area of a Circle = πr2 = 301.84 cm2
(22/7) × r2 = 301.84
r2 = 96.04
r = √96.04 = 9.8cm
Radius = 9.8 cm.
Circumference of a circle = 2πr
= 2 × (22/7) × 9.8
= 61.6 cm
Therefore, the circumference of the circle = 61.6 cm.
问题3.找到一个圆周为44厘米的圆的面积。
解决方案：
Circumference = 44 cm
2πr = 44 cm
2 × (22/7) × r = 44
r = 7 cm
Area of a Circle = πr2
= (22/7) × 7 × 7
= 154 cm2
Therefore, area of the Circle = 154 cm2
问题4.圆的周长超过直径16.8厘米。找到圆的周长。
解决方案：
Let the radius of the circle be r cm
Diameter (d) = 2r
Circumference of a circle (C) = 2πr
C = d + 16.8
2πr = 2r + 16.8
2πr – 2r = 16.8
2r (π – 1) = 16.8
2r (3.14 – 1) = 16.8
r = 3.92 cm
Radius = 3.92 cm
Circumference (C) = 2πr
C = 2 × 3.14 × 3.92
= 24.62 cm
Therefore, circumference of the circle = 24.64 cm.
问题5.一种马是依赖于用28米长的字符串一极。找到可以放牧马匹的区域。
解决方案：
Length of the string = 28 m
Area the horse can graze is the area of the circle with a radius equal to the length of the string.
Area of a Circle = πr2
= (22/7) × 28 × 28
= 2464 m2
Therefore, the area where horse can graze = 2464 m2
问题6.钢丝以正方形形式弯曲时，其面积为121 cm 2 。如果同一根线以圆形弯曲，则找到该圆形的区域。
解决方案：
Area of the square = a2
= 121 cm2
Area of the circle = πr2
121 cm2 = a2
Therefore, a = 11 cm
Perimeter of square = 4a
= 4 × 11 = 44 cm
Perimeter of the square = Circumference of the circle
Circumference = 2πr
44 = 2(22/7)r
r = 7 cm
Area of the Circle = πr2
= (22/7) × 7 × 7
= 154 cm2
Therefore, the area of the circle = 154 cm2.
问题7：两个圆的周长之比为2：3。找到他们的面积比例。
解决方案：
Circumference of a circle (C) = 2πr
Circumference of first circle = 2πr1
Circumference of second circle = 2πr2.
2πr1 : 2πr2 = 2:3
Therefore,
r1: r2 = 2: 3
Area of circle 1 = (πr1)2
Area of circle 2 = (πr2)2
Ratio = 22:32
= 4/9
Therefore, ratio of areas = 4: 9.
问题8.两个圆的半径之和为140厘米，圆周差为88厘米。找到圆的直径。
解决方案：
Sum of radii of two circles i.e., r1 + r2 = 140 cm … (i)
Difference of their circumference,
C1 – C2 = 88 cm
2πr1 – 2πr2 = 88 cm
2(22/7)(r1 – r2) = 88 cm
(r1 – r2) = 14 cm
r1 = r2 + 14….. (ii)
From (i) and (ii)
r2 + r2 + 14 = 140
2r2 = 140 – 14
2r2 = 126
r2 = 63 cm
r1 = 63 + 14 = 77 cm
Therefore,
Diameter of circle 1 = 2 x 77 = 154 cm
Diameter of circle 2 = 2 × 63 = 126 cm
问题9.求出一个圆的半径，该圆的周长等于两个半径为15cm和18cm的圆的周长之和。
解决方案：
Radius of circle 1 = r1 = 15 cm
Radius of circle 2 = r2 = 18 cm
C1 = 2πr1 , C2 = 2πr2
C = C1 + C2
2πr = 2πr1 + 2πr2
r = r1 + r2
r = 15 + 18
r = 33 cm
Therefore, the radius of the circle = 33 cm
问题10.两个圆的半径分别是8厘米和6厘米。求出其面积等于两个圆的面积之和的圆的半径。
解决方案：
Radii of the two circles are 6 cm and 8 cm
Area of circle with radius 8 cm = π (8)2
= 64π cm2
Area of circle with radius 6cm = π (6)2
= 36π cm2
Sum of areas = 64π + 36π = 100π cm2
Let the radius of the circle be r cm
Area of the circle = 100π cm2
πr2 = 100π
r= √100 = 10 cm
Therefore, the radius of the circle = 10 cm.