This is the Multiple Choice Questions Part 2 of the Series in Solid 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.

### Multiple Choice Questions Topic Outline

- MCQs in Polyhedrons | MCQs in Platonic Solids | MCQs in Cube | MCQs in Rectangular Parallelepiped | MCQs in Prism | MCQs in Cylinders | MCQs in Pyramids and Cones | MCQs in Frustum of Pyramids/Cones | MCQs in Prismatoid | MCQs in Sphere | MCQs in Zone | MCQs in Spherical Segment, Spherical Sector, Spherical Pyramid and Spherical Wedge | MCQs in Torus | MCQs in Ellipsoid and Spheroid

### Online Questions and Answers in Solid Geometry Series

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

**Solid Geometry MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

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

**PART II**

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

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

51. The frustum of a regular triangular pyramid has equilateral triangles for its bases. The lower and upper base edges are 9 m and 3 m, respectively. If the volume is 118.2 cu. m.., how far apart are the base?

- A. 9m
- B. 8m
- C. 7m
- D. 10m

52. A cylindrical gasoline tank, lying horizontally, 0.90 m. in diameter and 3 m long is filled to a depth of 0.60 m. How many gallons of gasoline does it contain? Hint: One cubic meter = 265 gallons

- A. 250
- B. 360
- C. 300
- D. 270

53. A closed cylindrical tank is 8 feet long and 3 feet in diameter. When lying in a horizontal position, the water is 2 feet deep. If the tank is the vertical position, the depth of water in the tank is:

- A. 5.67 m
- B. 5.82 m
- C. 5.82 ft
- D. 5.67 ft

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

- A. 5
- B. 4.5
- C. 69.08
- D. 4

55. If 23 cubic meters of water are poured into a conical vessel, it reaches a depth of 12 cm. how much water must be added so that the length reaches 18 cm.?

- A. 95 cubic meters
- B. 100 cubic meters
- C. 54.6 cubic meters
- D. 76.4 cubic meters

56. The height of a right circular base down is h. If it contains water to depth of 2h/3 the ratio of the volume of water to that of the cone is:

- A. 1:27
- B. 2:3
- C. 8:27
- D. 26:27

57. A right circular cone with an altitude of 9m is divided into two segments; one is a smaller circular cone having the same vertex with an altitude of 6m. Find the ratio of the volume of the two cones.

- A. 19:27
- B. 2:3
- C. 1:3
- D. 8:27

58. 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 its vertex. Find the volume of its content in cc.

- A. 387.4
- B. 381.7
- C. 383.5
- D. 385.2

59. A right circular cone with an altitude of 8 cm is divided into two segments. One is a smaller circular cone having the same vertex with the volume equal to ¼ of the original cone. Find the altitude of the smaller cone.

- A. 4.52 cm
- B. 6.74 cm
- C. 5.04 cm
- D. 6.12 cm

60. The slant height of a right circular cone is 5m long. The base diameter is 6m. What is the lateral area in sq. m?

- A. 37.7
- B. 47
- C. 44
- D. 40.8

61. A right circular cone has a volume of 128Ï€/3 cm^{3} and an altitude of 8 cm. The lateral area is:

- A. 16√5 Ï€ cm
^{2} - B. 12√5 Ï€ cm
^{2} - C. 16Ï€ cm
^{2} - D. 15Ï€ cm
^{2}

62. The volume of a right circular cone is 36Ï€. If its altitude is 3, find its radius.

- A. 3
- B. 4
- C. 5
- D. 6

63. A cone and hemisphere share base that is a semicircle with radius 3 and the cone is inscribed inside the hemisphere. Find the volume of the region outside the cone and inside the hemisphere.

- A. 24.874
- B. 27.284
- C. 28.274
- D. 28.724

64. A cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with a central angle of 210°. What is the volume of the cone in cc?

- A. 13,602
- B. 13,504
- C. 13,716
- D. 13,318

65. A cone was formed by rolling a thin sheet of metal in the form of a sector of a circle 72 cm in diameter with a central angle of 150°. Find the volume of the cone in cc.

- A. 7733
- B. 7722
- C. 7744
- D. 7711

66. A chemist’s measuring glass is conical in shape. If it is 8 cm deep and 3 cm across the mouth, find the distance on the slant edge between the markings for 1 cc and 2 cc.

- A. 0.82 cm
- B. 0.79 cm
- C. 0.74 cm
- D. 0.92 cm

67. The base areas of a frustum of a cone are 25 sq. cm. and 16 sq. cm, respectively. If its altitude is 6 cm, find its volume.

- A. 120 cm
^{3} - B. 122 cm
^{3} - C. 129 cm
^{3} - D. 133 cm
^{3}

68. What is the surface area of a sphere whose volume is 36 cu. m?

- A. 52.7 m
^{2} - B. 48.7 m
^{2 } - C. 46.6 m
^{2} - D. 54.6 m
^{2}

69. If the surface area of a sphere is increased by 21%, its volume is increased by:

- A. 13.31%
- B. 33.1%
- C. 21%
- D. 30%

70. The surface area of the sphere is 4Ï€r^{2}. Find the percentage increase in its diameter when the surface area increases by 21%.

- A. 5%
- B. 10%
- C. 15%
- D. 20%

71. Find the percentage increase in volume of a sphere if its surface area is increased by 21%

- A. 30.2%
- B. 33.1%
- C. 34.5%
- D. 30.9%

72. The volume of a sphere is increased by how much if its surface area is increased by 20%?

- A. 32.6%
- B. 33%
- C. 44%
- D. 72.8%

73. Given two spheres whose combined volume is known to be 819 cu. m. if their radii are in the ratio 3:4, what is the volume of the smaller sphere?

- A. 576 cu. m.
- B. 243 cu. m.
- C. 343 cu. m.
- D. 476 cu. m.

74. How much will the surface area of a sphere be increased if its radius is increased by 5%?

- A. 25%
- B. 15.5%
- C. 12.5%
- D. 10.25%

75. The volume of a sphere is 904.78 cu. m. Find the volume of the spherical segment of height 4 m.

- A. 234.57 cu. m.
- B. 256.58 cu. m.
- C. 145.69 cu. m.
- D. 124.58 cu. m.

76. A sphere of radius r just fits into a cylindrical container of radius r and altitude 2r. Find the empty space in the cylinder.

- A. (8/9)Ï€r
^{3} - B. (20/27)Ï€r
^{3} - C. (4/5)Ï€r
^{3} - D. (2/3)Ï€r
^{3}

77. If a solid steel ball is immersed in an eight cm. diameter cylinder, it displaces water to a depth of 2.25 cm. the radius of the ball is:

- A. 3 cm
- B. 6 cm
- C. 9 cm
- D. 12 cm

78. The diameter of two spheres is in the ratio 2:3. If the sum of their volumes is 1,260 cu. m., the volume of the larger sphere is:

- A. 972 cu. m.
- B. 927 cu. m.
- C. 856 cu. m.
- D. 865 cu. m.

79. A hemispherical bowl of radius 10 cm is filled with water to such a depth that the water surface area is equal to 75Ï€ cm^{2} The volume of water is:

- A. 625/3 cm
^{3} - B. 625Ï€/3 cm
^{3} - C. 625Ï€/2 cm
^{3} - D. 625Ï€ cm
^{3}

80. A water tank is in the form of a spherical segment whose base radii are 4 m and 3 m and whose altitude is 6 m. The capacity of the tank in gallon is:

- A. 91,011
- B. 92,011
- C. 95,011
- D. 348.72

81. Find the volume of a spherical sector of altitude 3 cm. and radius 5 cm.

- A. 75Ï€ cu. cm.
- B. 100Ï€ cu. cm.
- C. 50Ï€ cu. cm.
- D. 25Ï€ cu. cm.

82. How far from the center of a sphere of a radius 10 cm should a plane be passed so that the ratio of the areas of two zones is 3:7?

- A. 3 cm
- B. 4 cm
- C. 5 cm
- D. 6 cm

83. A 2-m diameter spherical tank contains1396 liter of water. How many liters of water must be added for the water to reach a depth of 1.75 m?

- A. 2613
- B. 2723
- C. 2542
- D. 2472

84. Find the volume of a spherical segment of radius 10 m and the altitude 5 m.

- A. 654.5 cu. m.
- B. 659.8 cu. m.
- C. 675.2 cu. m.
- D. 680.5 cu. m.

85. Find the volume of a spherical wedge of radius 10 cm. and central angle 50°.

- A. 425.66 sq. m.
- B. 431.25 sq. m.
- C. 581.78 sq. m.
- D. 444.56 sq. m.

86. Determine the area of the zone of a sphere of radius 8 in. and altitude 12 in.

- A. 192Ï€ sq. in.
- B. 198Ï€ sq. in.
- C. 185Ï€ sq. in.
- D. 195Ï€ sq. in.

87. The corners of a cubical block touch the closed spherical shell that encloses it. The volume of the box is 2744 cc. What volume in cc, inside the shell is not occupied by the block?

- A. 1356 cm
^{3} - B. 4721 cm
^{3} - C. 3423 cm
^{3} - D. 7623 cm
^{3}

88. A cubical container that measures 2 inches on each 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.

89. The volume of the water is a spherical tank is 1470.265 cm^{3}. Determine the depth of water if the tank has a diameter of 30 cm.

- A. 8
- B. 6
- C. 4
- D. 10

90. The volume of water in a spherical tank having a diameter of 4 m. is 5.236 m^{3}. Determine the depth of the water on the tank.

- A. 1.0
- B. 1.4
- C. 1.2
- D. 1.6

91. A mixture compound from 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”. 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”, find the radius of the bowl in inches.

- A. 7.53
- B. 7.33
- C. 7.73
- D. 7.93

92. 20.5 cubic meters of water is inside a spherical tank whose radius is 2 m. find the height of the water surface above the bottom of the tank, in m.

- A. 2.7
- B. 2.5
- C. 2.3
- D. 2.1

93. The volume of the sphere is 3Ï€ cu. m. The surface area of this sphere in sq. m. is:

- A. 36Ï€
- B. 24Ï€
- C. 18Ï€
- D. 12Ï€

94. Spherical balls 1.5 cm in diameter area packed in a box measuring 6 cm by 3 cm by 3 cm. If as many balls as possible are packed in the box, how much free space remains in the box?

- A. 28.41 cc
- B. 20.47 cc
- C. 29.87 cc
- D. 25.73 cc

95. A solid has a circular base of radius r. find the volume of the solid if every plane perpendicular to a given diameter is a square.

- A. 16 r
^{3}/3 - B. 5 r
^{3} - C.
^{}6 r^{3} - D. 19 r
^{3}/3

96. A solid has circular base of diameter 20 cm. Find the volume of the solid if every cutting plane perpendicular to the base along a given diameter is an equilateral triangle.

- A. 2514 cc
- B. 2107 cc
- C. 2309 cc
- D. 2847 cc

97. The base of a certain solid is a triangle of base b and altitude h. if all sections perpendicular to the altitude of the triangle are regular hexagons, find the volume of the solid.

98. The volume generated by the circle by the circle x^{2} + y^{2} + 4x – 6y – 12 = 0 revolved about the line 2x – 3y – 12 = 0 is:

- A. 3242 cubic units
- B. 3342 cubic units
- C. 3452 cubic units
- D. 3422 cubic units

99. The volume generated by rotating the curve 9x^{2} + 4y^{2} = 36 about the line 4x + 3y = 20 is:

- A. 48Ï€
- B. 58Ï€
^{2} - C. 42Ï€
- D. 48Ï€
^{2}

100. Find the volume generated by revolving the area bounded by the ellipse (y^{2}/9) + (x^{2}/4) = 1 about the line x = 3.

- A. 347.23 cu. units
- B. 355.31 cu. units
- C. 378.43 cu. units
- D. 389.51 cu. units

101. The area in the second quadrant of the circle x^{2} + y^{2} = 36 is revolved about the line y + 10 = 0. What is the volume generated?

- A. 2218.6
- B. 2228.8
- C. 2233.4
- D. 2208.5

102. A square area of edge “a” revolves about a line through one vertex, making an angle Ñ² with an edge and not crossing the square. Find the volume generated.

- A. 3Ï€ a
^{3}(sin Ñ² + cos Ñ²) - B. Ï€ a
^{3}(sin Ñ² + cos Ñ²) / 2 - C. 2Ï€ a
^{3}(sin Ñ² + cos Ñ²) - D. Ï€ a
^{3}(sin Ñ² + cos Ñ²)

103. Given an ellipse whose semi-major axis is 6 cm. and semi-minor axis is 3 cm. what is the volume generated if it is revolved about the minor axis?

- A. 36Ï€ cu. cm.
- B. 72Ï€ cu. cm.
- C. 96Ï€ cu. cm
- D. 144Ï€ cu. cm

104. A square hole 2” x 2” is cut through a 6-inch diameter long along its diameter and perpendicular to its axis. Find the volume of wood that was removed.

- A. 27.32 cu. in.
- B. 23.54 cu. in.
- C. 21.78 cu. in.
- D. 34.62 cu. in.

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