# MCQ in Geometry Part 2 | Mathematics Board Exam

(Last Updated On: January 11, 2021) This is the Multiple Choice Questions Part 2 of the Series in 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 Mathematics Board Exam Syllabi

• MCQ in Lines and Planes | MCQ in lane figures | MCQ in Application of Cavalier’s, Pappus and Prismodial Theorems | MCQ in Coordinate in Space | MCQ in Quadratic Surfaces | MCQ in Mensuration | MCQ in Plane Geometry | MCQ in Solid Geometry | MCQ in Spherical Geometry | MCQs in Analytical Geometry

#### Continue Practice Exam Test Questions Part 2 of the Series

Choose the letter of the best answer in each questions.

51. A circular piece of a cardboard with a diameter of 1 m will be made into a conical hat 40 cm high by cutting a sector off and joining the edges to form a cone. Determine the angle subtended by the sector removed.

a. 144°

b. 148°

c. 152°

d. 154°

Solution:

52. What is the area in sq. m of the zone of a spherical segment having a volume of 1470.265 cu. M if the diameter of the sphere is 30 m?

a. 465.5 sq. m

b. 565.5 sq. m

c. 665.5 sq. m

d. 656.5 sq. m

Solution:

53. A sphere having a diameter of 30 cm is cut into 2 segments. The altitude of the first segment is 6 cm. What is the ratio of the area of the second segment to that of the first?

a. 4:1

b. 3:1

c. 2:1

d. 3:2

Solution:

54. If the edge of a cube is increased by 30% by how much is the surface area increased?

a. 30%

b. 33%

c. 60%

d. 69%

Solution:

55. Each side of a cube is increased by 1%. By what percent is the volume of the cube increased?

a. 1.21%

b. 2.8%

c. 3.03%

d. 3.5%

Solution:

56. Given a sphere of a diameter, d. What is the percentage increase in its diameter when the surface area is increases by 21%?

a. 5%

b. 10%

c. 21%

d. 33%

Solution:

57. Given a sphere of a diameter, d. What is the percentage increase in its volume when the surface area is increases by 21%?

a. 5%

b. 10%

c. 21%

d. 33%

Solution:

58. How many times do the volume of a sphere increases if the radius is doubled?

a. 4 times

b. 2 times

c. 6 times

d. 8 times

Solution:

59. A circular cone having an altitude of 9 m is divided into 2 segments having the same vertex. If the smaller altitude is 6 m, find the ratio of the volume of the small cone to the big cone.

a. 0.186

b. 0.296

c. 0.386

d. 0.486

Solution:

60. Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of 210°

a. 12367.2 sq. cm

b. 13232.6 sq. cm

c. 13503.4 sq. cm

d. 14682.5 sq. cm

Solution:

61. Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of 150°

a. 5533.32 sq. cm

b. 6622.44 sq. cm

c. 7710.82 sq. cm

d. 8866.44 sq. cm

Solution:

62. A conical vessel has a height of 24 cm and a base diameter of 12 cm. it holds water to a depth of 18 cm above the vertex. Find the volume in sq. cm of its content

a. 188.40

b. 298.40

c. 381.70

d. 412.60

Solution:

63. What is the height of a right circular cone having a slant height of sqrt(10x) and a base diameter of 2x?

a. 2x

b. 3x

c. 3.317x

d. 3.162x

Solution:

64. The ratio of the volume to the lateral area of a right circular cone is 2:1. If the altitude is 5 cm, what is the ratio of the slant height to the radius?

a. 5:6

b. 5:4

c. 5:3

d. 5:2

Solution:

65. A regular triangular pyramid has an altitude of 9 m and a volume of 187.06 cu. m. What is the base edge in meters?

a. 12

b. 13

c. 14

d. 15

Solution:

66. The volume of the frustum of a regular triangular pyramid is 135 cu. m. The lower base is an equilateral triangle with an edge of 9 m. The upper base is 8 m above the lower base. What is the upper base edge in meters?

a. 2

b. 3

c. 4

d. 5

Solution:

67. What is the volume of a frustum of a cone whose upper base is 15 cm in diameter and lower base 10 cm. in diameter with an altitude of 25 cm?

a. 3018.87 cu. cm

b. 3180.87 cu. cm

c. 3108.87 cu. cm

d. 3081.87 cu. cm

Solution:

68. In a portion of an electrical railway cutting, the areas of cross section taken every 50 m are 2556, 2619, 2700, 2610 and 2484 sq. m. Find its volume.

a. 522,600 cu. m

b. 520, 500 cu. m

c. 540,600 cu. m

d. 534,200 cu. m

Solution:

69. Determine the volume of a right truncated triangular prism with the following definitions: let the corners of the triangular base be defined by A, B and C. The length of AB = 10 ft., BC = 9 ft., and CA = 12 ft. The sides A, B and C are perpendicular to the triangular base and have the height of 8.6 ft., 7.1 ft., 5.5 ft., respectively.

a. 413 sq. ft

b. 311 sq. ft

c. 313 sq. ft

d. 391 sq. ft

Solution:

70. A circular cylinder with a volume of 6.54 cu. m is circumscribed about a right prism whose base is an equilateral triangle of side 1.25 m. What is the altitude of the cylinder in meters?

a. 3.50

b. 3.75

c. 4.00

d. 4.25

Solution:

71. A circular cylinder is circumscribed about a right prism having a square base cone meter on an edge. The volume of the cylinder is 6.283 cu. m. Find its altitude in meters

a. 4.00

b. 3.75

c. 6.50

d. 3.25

Solution:

72. The bases of a right prism are hexagons with one of each side equal to 6 cm. The bases are 12 cm apart. What is the volume of the right prism?

a. 1211.6 cu. cm

b. 2211.7 cu. cm

c. 1212.5 cu. cm

d. 1122.4 cu. cm

Solution:

73. Two vertical conical tanks are joined at the vertices by a pipe. Initially the bigger tank is full of water. The pipe valve is open to allow the water to flow to the smaller tank until it is full. At this moment, how deep is the water in the bigger tank? The bigger tank has a diameter f 6 ft. and a height of 10 ft., the smaller tank has a diameter of 6 ft. and a height of 8 ft. Neglect the volume of water in the pipeline.

a. 200(1/3)

b. 50(1/3)

c. 25(1/3)

d. 50(1/4)

Solution:

74. The central angle of a spherical wedge is 1 radian. Find its volume if its radius is 1 unit.

a. 2/3

b. 1/2

c. 3/4

d. 2/5

Solution:

75. A regular octahedron has an edge 2 m. find its volume in cu. m.

a. 3.77

b. 1.88

c. 3.22

d. 2.44

Solution:

76. A mixture compound of equal parts of two liquids, one white and the other black, was placed in a hemispherical bowl. The total depth of the two liquids is 6 inches. After standing for a short time, the mixture separated, the white liquid settling below the black. If the thickness of the segment of the black liquid is 2 inches, find the radius of the bowl in inches.

a. 7.33

b. 7.53

c. 7.73

d. 7.93

Solution:

77. The volume of water in a spherical tank having a diameter of 4 m is 5.236 cu. m. Determine the depth of the water in the tank.

a. 1.0

b. 1.2

c. 1.4

d. 1.8

Solution:

78. An ice cream cone is filled with ice cream and a surmounted ice cream in the form of a hemisphere on top of the cone. If the hemispherical surface is equal to the lateral area of the cone, find the total volume in cu. inches of ice cream if the radius of the hemisphere is 1 inch and assuming the diameter of hemisphere is equal to the diameter of the cone.

a. 3.45

b. 3.91

c. 4.12

d. 4.25

Solution:

79. A cubical container that measures 2 inches on a side is tightly packed with 8 marbles and is filled with water. All 8 marbles are in contact with the walls of the container and the adjacent marbles. All of the marbles are of the same size. What is the volume of water in the container?

a. 0.38 cu. in.

b. 2.5 cu. in.

c. 3.8 cu. in.

d. 4.2 cu. in.

Solution:

80. The corners of a cubical block touched the closed spherical shell that encloses it. The volume of the box is 2744 cubic cm. What volume in cubic centimeter inside the shell is not occupied by the block?

a. 2714.56

b. 3714.65

c. 4713.56

d. 4613.74

Solution:

81. The linear distance between -4 and 17 on the number line is

A. 13

B. 21

C. -17

D. -13

Solution:

82. Find the distance between A (4, -3) and B (-2, 5).

A. 11

B. 9

C. 10

D. 8

Solution:

83. If the distance between points (3, y) and (8, 7) is 13, then y is equal to

A. 5 or -5

B. 5 or 19

C. 19

D. -5 or 19

Solution:

84. Find the coordinates of a point equidistant from (1, -6), (5, 6) and (6, -1).

A. (2, -2)

B. (3, -2)

C. (3, -3)

D. (2, -3)

Solution:

85. The line segment connecting (x, 6) and (9, y) is bisected by the point (7, 3). Find the values of x and y.

A. 14, 6

B. 33, 12

C. 5, 0

D. 14, 6

Solution:

86. If (-2, -4) is the midpoint of (6, -7) and (x, y), then the values of x and y are

A. x = 2, y = 1

B. x = -10, y = -1

C. x = 10, y = -1

D. x = -8, y = -1

Solution:

87. Determine the coordinates of the point which is three-fifths of the way from the point (2, -5) to the point (-3, 5).

A. (-1, 1)

B. (-2, -1)

C. (-1, -2)

D. (1, -1)

Solution:

88. The segment from (-1, 4) to (2, -2) is extended three times its own length. The terminal point is

A. (11, -24)

B. (-11, -20)

C. (11, -18)

D. (11, -20)

Solution:

89. The points (a,1), (b,2) and (c,3) are collinear. Which of the following is true?

A. c –b = c – a

B. c – b = b – a

C. c – a = a – b

D. c – a = b – a

Solution:

90. If the slope of the line connecting the origin and point P is 3/4, find the abscissa of P if its ordinate is 6.

A. 2

B. 6

C. 7

D. 8

Solution:

91. Find the inclination of the line passing through (-5, 3) and 10, 7).

A. 14.73

B. 14.93

C. 14.83

D. 14.63

Solution:

92. Find the angle formed by the lines 2x + y – 8 = 0 and x + 3y + 4 = 0.

A. 30°

B. 35°

C. 45°

D. 60°

Solution:

93. Find the angle between lines 3x + 2y = 6 and x + y = 6.

A. 12°20’

B. 11°19’

C. 14°25’

D. 13°06’

Solution:

94. What is the acute angle between the lines y = 3x + 2 and y = 4x + 9?

A. 4.4°

B. 28.3°

C. 5.2°

D. 18.6°

Solution:

95. Find the distance of the line 3x + 4y = 5 from the origin.

A. 4

B. 3

C. 2

D. 1

Solution:

96. The two points on the line s 2x = 3y + 4 = 0 which are at a distance 2 from the line 3x + 4y – 6 = 0 are

A. (-5, 1) and (-5, 2)

B. (64, -44) and (4, -4)

C. (8, 8) and (12, 12)

D. (44, -64) and (-4, 4)

Solution:

97. The distance from the point (2, 1) to the line 4x – 3y + 5 = 0 is

A. 1

B. 2

C. 3

D. 4

Solution:

98. Determine the distance from (5, 10) to the line x – y = 0.

A. 3.33

B. 3.54

C. 4.23

D. 5.45

Solution:

99. The distance from a point (1, 3) to the line 4x + 3y + 12 = 0 is

A. 4 units

B. 5 units

C. 6 units

D. 7 units

Solution:

100. Find the distance between the given lines 4x – 3y = 12 and 4x – 3y = -8.

A. 3

B. 4

C. 5

D. 6

Solution:

### Online Question and Answer in Geometry Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Geometry
PART 1: MCQ from Number 1 – 50                                                               Answer key: PART 1
PART 2: MCQ from Number 51 – 100                                                           Answer key: PART 2
PART 3: MCQ from Number 101 – 150                                                         Answer key: PART 3
PART 4: MCQ from Number 151 – 200                                                         Answer key: PART 4
PART 5: MCQ from Number 201 – 250                                                         Answer key: PART 5