This is the Multiple Choice Questions Part 3 of the Series in Plane Geometry topic in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

#### MCQ Topic Outline included in ME Board Exam Syllabi

- MCQ in Venn Diagram | MCQ in Definition of Plane Geometry | MCQ in Angles | MCQ in Circles | MCQ in Ellipse | MCQ in Polygons | MCQ in Triangles | MCQ in Quadrilaterals | MCQ in Trapezoids and Trapeziums | MCQ in Parallelograms | MCQ in Square and Rectangles | MCQ in Rhomboid and Rhombus

#### Continue Practice Exam Test Questions Part 3 of the Series

⇐ MCQ in Plane Geometry Part 2 | Mathematics Board Exam

**Choose the letter of the best answer in each questions.**

101. The angle of a sector is 30 degrees and the radius is 15 cm. What is the area of the sector?

A. 89.5 cm^{2}

B. 58.9 cm^{2}

C. 59.8 cm^{2}

D. 85.9 cm^{2}

Answer: **Option B**

Solution:

102. A sector has a radius of 12 cm. if the length of its arc is 12 cm, its area is:

A. 66 sq. cm.

B. 82 sq. cm.

C. 144 sq. cm.

D. 72 sq. cm.

Answer: **Option D**

Solution:

103. The perimeter of a sector is 9 cm and its radius is 3 cm. What is the area of the sector?

A. 4 cm^{2}

B. 9/2 cm^{2}

C. 11/2 cm^{2}

D. 27/2 cm^{2}

Answer: **Option B**

Solution:

104. A swimming pool is to be constructed in the space of partially overlapping identical circles. Each of the circles has a radius of 9 m, and each passes through the center of the other. Find the area of the swimming pool.

A. 302.33 m^{2}

B. 362.55 m^{2}

C. 398.99 m^{2}

D. 409.44 m^{2}

Answer: **Option D**

Solution:

105. Given are two concentric circles with the outer circle having a radius of 10 cm. If the area of the inner circle is half of the outer circle, find the boarder between the two circles.

A. 2.930 cm

B. 2.856 cm

C. 3.265 cm

D. 2.444 cm

Answer: **Option A**

Solution:

106. A circle of radius 5 cm has a chord which is 6cm long. Find the area of the circle concentric to this circle and tangent to the given chord.

A. 14π

B. 16π

C. 9π

D. 4π

Answer: **Option B**

Solution:

107. A reversed curve on a railroad track consists of two circular arcs. The central angle of one side is 20° with radius 2500 feet, and the central angle of the other is 25° with radius 3000 feet. Find the total lengths of t he two arcs.

A. 2812 ft.

B. 2218 ft.

C. 2821 ft.

D. 2182 ft.

Answer: **Option D**

Solution:

108. Given a triangle whose sides are 24 cm, 30 cm, and 36 cm. find the radius of a circle which is tangent to the shortest and longest side of the triangle, and whose center lies on the third side.

A. 9.111 cm

B. 11.91 cm

C. 12.31 cm

D. 18 cm

Answer: **Option B**

Solution:

109. Find the area of the largest circle that can be cut from a triangle whose sides are 10 cm, 18 cm, and 20 m.

A. 11π cm^{2}

B. 12π cm^{2}

C. 14π cm^{2}

D. 15π cm^{2}

Answer: **Option C**

Solution:

110. The diameter of the circle circumscribed about a triangle ABC with sides a, b , c is equal to:

A. a/sin A

B. b/sin B

C. c/sin C

D. all of these

Answer: **Option D**

Solution:

111. The sides of a triangle are 14 cm., 15 cm., and 13 cm. find the area of the circumscribing circle.

A. 207.4 sq. cm.

B. 209.6 sq. cm.

C. 215.4 sq. cm.

D. 220.5 sq. cm.

Answer: **Option A**

Solution:

112. What is the radius of the circle circumscribing an isosceles right triangle having an area of 162 sq. cm?

A. 13.52

B. 14.18

C. 12.73

D. 1564

Answer: **Option C**

Solution:

113. If the radius of the circle is decreased by 20%, by how much is its area decreased?

A. 36%

B. 26%

C. 46%

D. 56%

Answer: **Option A**

Solution:

114. The distance between the center of the three circles which are mutually tangent to each other externally are 10, 12 and 14 units. The area of the of the largest circle is:

A. 72π

B. 23π

C. 64π

D. 16π

Answer: **Option C**

Solution:

115. The sides of a cyclic quadrilateral measures 8 cm, 9 cm, 12 cm, and 7 cm, respectively. Find the area of the circumscribing circle.

A. 8.65 cm^{2}

B. 186.23 cm^{2}

C. 6.54 cm^{2}

D. 134.37 cm^{2}

Answer: **Option D**

Solution:

116. The wheel of a car revolves n times, while the car travels x km. the radius of the wheel in meter is:

A. 10,000 x/(π n)

B. 500 x/(π n)

C. 500,00 x/(π n)

D. 5,000 x/(π n)

Answer: **Option B**

Solution:

117. If the inside wheels of a car running a circular track are going half as fast as the outside wheel, determine the length of the track, described by the outer wheels, if the wheels are 1.5 m apart.

A. 4π

B. 5π

C. 6π

D. 8π

Answer: **Option C**

Solution:

118. A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft long and the goat can reach 1 ft farther than the rope length, what is the maximum area the goat can cover?

A. 5281 ft^{2}

B. 4084 ft^{2}

C. 3961 ft^{2}

D. 3970 ft^{2}

Answer: **Option B**

Solution:

119. The interior angles of a triangle measures 2x, x + 15, and 2x + 15. What is the value of x?

A. 30°

B. 66°

C. 42°

D. 54°

Answer: **Option A**

Solution:

120. Two complementary angles are in the ratio 2:1. Find the larger angle.

A. 30°

B. 60°

C. 75°

D. 15°

Answer: **Option B**

Solution:

121. Two transmission towers 40 feet high is 200 feet apart. If the lowest point of the cable is 10 feet above the ground, the vertical distance from the roadway to the cable 50 feet from the center is:

A. 17.25 feet

B. 17.5 feet

C. 17.75 feet

D. 18 feet

Answer: **Option B**

Solution:

122. What is the area bounded by the curves y^{2} = 4x and x^{2} = 4y

A. 6.0

B. 7.333

C. 6.666

D. 5.333

Answer: **Option D**

Solution:

123. What is the area between y = 0, y = 3x^{2} , x = 0, and x = 2?

A. 8

B. 12

C. 24

D. 6

Answer: **Option A**

Solution:

### Online Question and Answer in Plane Geometry Series

Following is the list of practice exam test questions in this brand new series:

**MCQ in Plane Geometry**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

**MCQ from Number 51 – 100**Answer key:

**PART 2**

**MCQ from Number 101 – 150**Answer key:

**PART 3**

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