Math topic中文

Area of a circle

Explore and master the formula for the area of a circle and solve simple real-world problems.

Practice questions

  1. 1定积分∫01(2x−x2)dx\int_{0}^{1}(\sqrt{2x{-}x^{2}})dx等于()({ }) A. π4\dfrac{\pi}{4} B. π2\dfrac{\pi}{2} C. π−14\dfrac{\pi{-}1}{4}…
  2. 2The figure is made up of a rectangle, a square and a quadrant. Find the area of the shaded part. (Take π=3.14\pi = 3.14) Ans…
  3. 3用同样长的绳子分别围长方形、正方形、圆，面积从小到大的排列是()(\quad) A. 圆<<正方形<<长方形 B. 正方形<<长方形<<圆 C. 圆>>正方形>>长方形 D. 长方形<<正方形<<…
  4. 4用44米长的绳子把一只羊拴在一根木桩上，这只羊吃草面积最大是()(\quad)平方米。 A. 4×2×3.144×2×3.14 B. 4×4×3.144×4×3.14 C. 3.14×23.14×2 D. 2×42×4
  5. 5一张长方形的纸，它的长是8厘米，宽是6厘米．（1）如果用它剪下一个最大的圆后，剩下的面积是多少平方厘米？（2）如果用它剪下一个最大的半圆，剩下的面积是多少平方厘米？
  6. 6The figure shows a 34\frac{3}{4} circle of radius 14 cm. Find the perimeter of the figure. (Take π=227\pi = \frac{22}{7}) A…
  7. 7The figure shows a circle and 6 identical quarter circles. The radius of each quarter circle is 8 cm. Line XY passes thr…
  8. 8The figure is formed by 3 identical quarter circles and a triangle. The radius of each quarter circle is 8 cm. Find the…
  9. 9The figure below is made up of a square and 4 semicircles. The perimeter of the figure is 20π20\pi cm. What is the perime…
  10. 10一个圆柱形水桶，底面直径3030厘米，高3535米，桶内装有1515厘米高的水。 (1)如果沿着桶口给这个水桶加一道铁箍，需要多长的铁丝？ (2)水与桶接触的面，面积一共是多少平方厘米？ (3)将一个圆锥形的铁块完全浸没水中，水…
  11. 11∫−22(sin⁡x+4−x2)dx=()∫_{-2}^{2}(\sin x+\sqrt{4-x^{2}}){\rm d}x=(\quad) A. 44 B. 2π2π C. 4+2π4+2π D. 88
  12. 12The figure shown is made up of rectangle ABCD, a circle with FG as the diameter, 2 identical small semi-circles with dia…
  13. 13A figure is drawn on a piece of square paper with length 40 cm as shown. The figure is made up of 1 large quarter circle…
  14. 14The figure below is made up of 2 identical quadrants of radius 7 cm that overlapped each other. The shaded square has si…
  15. 15Which two figures below have the same area? (Take π=227\pi = \frac{22}{7})
  16. 16The figure shows a quarter circle ABC and a rectangle CDEF. The length of AC is 10 cm. The sum of the lengths of EF and…
  17. 17下列各项中，两种量成比例的是()(\quad) A. 圆的面积和它的直径 B. 被减数一定，差与减数 C. 工作总量一定，工作效率和工作时间
  18. 18A semicircle was cut from a rectangle as shown below. The perimeter of the rectangle before it was cut was 56 cm. What i…
  19. 19已知△ABC\triangle ABC的内角AA，BB，CC的对边分别为aa，bb，cc，满足bcos⁡A+acos⁡B=2ccos⁡Bb\cos A+a\cos B=2c\cos B，b=23b=2\sqrt{3}，则△ABC\triangle ABC…
  20. 20圆的周长是18.84m18.84m，这个圆的直径是 ___ mm，面积是 ___ m2.m^{2}.
  21. 21The figure below is made up of 2 identical big quarter circles and 2 identical small quarter circles. The radius of the…
  22. 22有一块圆形绿地半径为 9 米，现在要缩小绿地面积，在中间挖走一块半径为 6 米的圆形绿地，使其成为一个圆环形绿地，缩小后的绿地面积是 （ ___ ） 平方米。
  23. 23若圆锥的底面半径为3cm3cm，母线长为5cm5cm，则这个圆锥的全面积为 ___ cm2.(cm^{2}.(结果保留π)π)
  24. 24The figure below is made up of a circle and a right-angled triangle XYZ. O is the centre of the circle. YOZ is a straigh…
  25. 25It is given that f(x)={4a2−x2for 0≤x≤2a,3x−6afor 2a<x<3a,f(x) = \begin{cases} \sqrt{4a^2 - x^2} & \text{for } 0 \le x \le 2a, \\ 3x - 6a & \text{for } 2a < x < 3a, \end{cases}…
  26. 26把一个圆平均分成若干份，然后把它剪开，拼成一个近似的长方形，已知长方形的长是15.7厘米，这个圆的面积是 （ ___ ） 。
  27. 27The figure is made up of a semicircle, a large circle and a small circle. O is the centre of the semicircle and the larg…
  28. 28Leon designed a logo as shown. The logo is made up of two identical small semi-circles, a circle and a big quadrant. YZ…
  29. 29一个长方形长和宽分别是6cm和4cm，在这个长方形内截取一个最大的圆后，剩余的面积是长方形面积的___ %．
  30. 30The figure is made up of a triangle in a semicircle of radius 5 cm. The sides of the triangle measure 4 cm, 3 cm and 5 c…
  31. 31The figure below is made up of a square, a quarter circle and a semicircle. The area of the square is 196 cm2^2. Find t…
  32. 32The figure below shows a circle drawn inside a square. A shaded square is then drawn inside the circle. What fraction of…
  33. 33把一个半径为22的圆分成三个扇形，使它们的圆心角的度数之比为1:3:5.(1)1:3:5.(1)求这三个扇形的圆心角的度数. (2)求这三个扇形的面积((结果保留π).\pi).
  34. 34一个圆柱的底面直径是6cm6cm，高是10cm10cm。它的侧面积是 ___cm2cm^{2}，表面积是 ___cm2cm^{2}。
  35. 35一个半径是 4cm 的半圆，它的周长是 （ ___ ） cm ，面积是 （ ___ ） cm 2 。
  36. 36一个圆锥的体积是50.24cm350.24cm^{3}，底面直径是8cm8cm，它的高是 ___ cmcm，和它等底等高的圆柱的体积是 ___ cm3cm^{3}。
  37. 37The figure below is made up of a quadrant and a circle overlapping each other. The quadrant touches the circle at points…
  38. 38The radius of Circle A is 3 times the radius of Circle B. Circle A makes 12 revolutions to roll from X to Y. (Take π=3.14\pi = 3.14…
  39. 39The figure is made up of 2 identical quarter circles in a rectangle. Find the perimeter of the shaded part. (Take π=3.14\pi = 3.14…
  40. 40圆的半径与面积()(\quad) A. 成正比例 B. 成反比例 C. 不成比例
  41. 41街心花园修建一个圆形花坛，周长是31.4米，在花坛的周围修建一条宽是1米的环形小路。这条小路的面积多少？
  42. 42The figure below is formed by 2 quadrants and a rectangle overlapping one another. The radius of the smaller quadrant is…
  43. 43一个圆的直径是4分米，这个圆的面积是___平方分米。
  44. 44把一个半径是r的圆平均分成若干份后，剪拼成一个近似长方形，这个长方形的周长是（ ） A. 2×（πr+r） B. 5.14r C. 8.28r D. 2πr
  45. 45The figure below is made up of four squares of sides 10 cm, four quadrants and eight semicircles. Find the total area of…
  46. 46做一个无盖的圆柱形铁皮桶，底面直径是40厘米，高5分米，做这个水桶大约用铁皮多少平方厘米？（得数保留整百平方厘米）
  47. 47The figure shows a cylinder which is hollow in the middle and has a thickness of 10 cm. (Taking π=3.14\pi = 3.14.) Find the…
  48. 48The figure is made up of 2 identical semicircles of diameter 14 cm. Find the perimeter of the figure. Take π=227\pi = \frac{22}{7}…
  49. 49Three parts of a circle with a radius of 14 cm is shaded. These three parts add up to a quarter of the circle. What is t…
  50. 50The figure below is made up of a rectangle ABCD and a semicircle. AEC is a straight line. The arc of the semicircle touc…
  51. 51在一个边长是6分米的正方形纸板上剪去一个最大的圆,圆的半径是 （ ___ ） 分米,圆的面积是 （ ___ ）分米 2 , 剩下部分的面积是（ ___ ） 平方分米.
  52. 52The shaded figure is made up of 6 big quarter arcs, 6 small quarter arcs and 2 straight lines. Find the area of the shad…
  53. 53(1)求经过点P(4,1)P(4,1)，且在两坐标轴上的截距相等的直线方程． (2)设直线y=x+2ay=x+2a与圆CC：x2+y2−2ay−2=0x^{2}+y^{2}-2ay-2=0相交于AA，BB两点，若∣AB∣=23|AB|=2\sqrt{3}…