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Geometry Questions: Solved 321 Geometry Questions and answers section with explanation for various online exam preparation, various interviews, Aptitude Category online test. Category Questions section with detailed description, explanation will help you to master the topic.
Geometry Questions
61. Find the circumference of the semicircle of radius 7.
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Correct Ans:22
Explanation:
Given, radius, r = 7
Circumference of the semicircle = pi * r
=> (22/7) * 7
= 22
Thus, Circumference of the semicircle = 22
Circumference of the semicircle = pi * r
=> (22/7) * 7
= 22
Thus, Circumference of the semicircle = 22
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62. Find the area of the sector which makes 90 degree at the center for the circle with radius 14 cm
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Correct Ans:154
Explanation:
Given, Ø = 90 deg
Area of sector = (Ø / 360 ) * pi * r^2
= (90 /360) * (22/7) * 14 * 14
= 22 * 7
= 154 cm^2
Thus, Area of sector = 154 cm^2
Area of sector = (Ø / 360 ) * pi * r^2
= (90 /360) * (22/7) * 14 * 14
= 22 * 7
= 154 cm^2
Thus, Area of sector = 154 cm^2
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63. Find the circumference of the semicircle of radius 2.
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Correct Ans:6.29
Explanation:
Given, radius = 2
Circumference of semicircle = pi * r
= (22/7) * 2
= 6.29
Therefore, Circumference of semicircle = 6.29
Circumference of semicircle = pi * r
= (22/7) * 2
= 6.29
Therefore, Circumference of semicircle = 6.29
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64. Find the circumference of the semicircle of radius 21.
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Correct Ans:66
Explanation:
Given, radius = 21
Circumference of semicircle = pi * r
= (22/7) * 21
= 66
Thus, Circumference of semicircle = 66
Circumference of semicircle = pi * r
= (22/7) * 21
= 66
Thus, Circumference of semicircle = 66
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65. If the ratio of areas of two circles are 16 : 25, then the ratio of the radii of the circle will be
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Correct Ans:(4 : 5)
Explanation:
Let r1 be the radius of one of the circle and
r2 be the radius of another circle.
Given, ratio of areas of two circles = 16 : 25
=> [pi * (r1)^2] : [pi * (r2)^2] = 16 : 25
=> r1 : r2 = sqrt(16) : srt(25)
=> r1 : r2 = 4 : 5
r2 be the radius of another circle.
Given, ratio of areas of two circles = 16 : 25
=> [pi * (r1)^2] : [pi * (r2)^2] = 16 : 25
=> r1 : r2 = sqrt(16) : srt(25)
=> r1 : r2 = 4 : 5
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66. Find the circumference of the semicircle of radius 14.
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Correct Ans:44
Explanation:
Given, radius of semicircle = 14
Circumference of semicircle = pi * r
= (22/7) * 14
= 44
Thus, Circumference of semicircle = 44
Circumference of semicircle = pi * r
= (22/7) * 14
= 44
Thus, Circumference of semicircle = 44
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67. Find the area of trapezium whose length of the parallel sides are 12 and 28 cm. If the distance between the parallel sides are given by 25 cm, then the area of the trapezium is
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Correct Ans:500
Explanation:
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68. Two circles of radius 3 cm and 4 cm, are drawn in such a way that they touch each other exactly at one point. A and B are two points on these two circles. If AB denotes the distance between them, then the maximum value of AB can be
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Correct Ans:16
Explanation:
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69. A wire in the form of a circle of radius 3.5 m is bent in the form of a rectangle, whose length and breadth are in the ratio of 6 : 5. What is the area of the rectangle?
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Correct Ans:30
Explanation:
Given, circle of radius (r) = 3.5 m
The circular wire is bent to form rectangle, which means
Circumference of circle = perimeter of rectangle
Circumference of circle = 2 * pi * r
= 2 * (22/7) * 3.5
= 22
=> perimeter of rectangle = 22
=> 2(length + breadth) = 22
Given, length and breadth are in the ratio of 6 : 5
=> length = 6x meters and breadth = 5x meters.
=> 2(6x + 5x) = 22
=> 11x = 11
=> x = 1
Then, length = 6x meters = 6 meters
and breadth = 5x meters = 5 meters
Area of rectangle = length X breadth
= 6 X 5
= 30
Therefore, Area of rectangle = 30 meters
The circular wire is bent to form rectangle, which means
Circumference of circle = perimeter of rectangle
Circumference of circle = 2 * pi * r
= 2 * (22/7) * 3.5
= 22
=> perimeter of rectangle = 22
=> 2(length + breadth) = 22
Given, length and breadth are in the ratio of 6 : 5
=> length = 6x meters and breadth = 5x meters.
=> 2(6x + 5x) = 22
=> 11x = 11
=> x = 1
Then, length = 6x meters = 6 meters
and breadth = 5x meters = 5 meters
Area of rectangle = length X breadth
= 6 X 5
= 30
Therefore, Area of rectangle = 30 meters
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70. Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm
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Correct Ans:285
Explanation:
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71.
A trapezium has a height of 5 cm and parallel sides of length 3 cm and 7 cm respectively. area of trapezium should be
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Correct Ans:25
Explanation:
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72. Find the area of the circle with equation x^2 + y^2 = 12
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Correct Ans:12pi
Explanation:
Given, equation of circle is: x^2 + y^2 = 12
The center-radius form of the circle equation is in the format(x–h)2+ (y–k)2=r2, with the center being at the point(h, k)and the radius being "r".
=> x^2 + y^2 = 12
=> (x – 0)^2 + (y – 0)^2 = 12
On comparing this eqn with the standard one: => (x–h)2+ (y–k)2=r2
Thus, r^2 = 12
Area of circle = pi * r^2
= pi * 12
= 12 pi
Thus, Area of circle = 12 pi
The center-radius form of the circle equation is in the format(x–h)2+ (y–k)2=r2, with the center being at the point(h, k)and the radius being "r".
=> x^2 + y^2 = 12
=> (x – 0)^2 + (y – 0)^2 = 12
On comparing this eqn with the standard one: => (x–h)2+ (y–k)2=r2
Thus, r^2 = 12
Area of circle = pi * r^2
= pi * 12
= 12 pi
Thus, Area of circle = 12 pi
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73. A circle of radius 7 units, make 3 complete revolutions. Find the distance it have covered?
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Correct Ans:132
Explanation:
Given, radius of the circle = 7 units
Distance covered = circumference of the circle * 3
= 2 * pi * r * 3
= 2 * (22/7) * 7 * 3
= 2 * 22 * 3
= 132
Therefore, Distance covered = 132
Distance covered = circumference of the circle * 3
= 2 * pi * r * 3
= 2 * (22/7) * 7 * 3
= 2 * 22 * 3
= 132
Therefore, Distance covered = 132
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74. Find the area of the circle whose coordinates are (2,3) , (7,1) and (3,5)
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Correct Ans:6
Explanation:
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75. In a triangle ABC, a circle which touches the edges of all three sides is called
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Correct Ans:in circle
Explanation:
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76. In a triangle a circle passes through the vertices of the triangle, then the circle is called as
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Correct Ans:cirumcircle
Explanation:
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77. In triangle ABC of sides a,b and c, the area of the triangle is
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Correct Ans:(bc sin A)/2
Explanation:
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78. Find the 25 % of sum of all the exterior angles of a cylic quadrilateral.
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Correct Ans:90
Explanation:
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79. Which of these following points lie on the circle x^2 + y^2 = 25
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Correct Ans:(1,sqrt(24))
Explanation:
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80. Find the center of the circle whose end points of the diameters are (2,10) and (6,2).
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Correct Ans:(4,6)
Explanation:
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