MCQ in Solid Geometry Part 1 | Mathematics Board Exam Practice

Multiple Choice Questions in Solid Geometry Part 1 | Mathematics Board Exam Practice

Solid geometry is one of those topics in Engineering Mathematics that looks straightforward on the surface but has a way of humbling you once the problems get specific. Volumes, surface areas, cross sections, and the relationships between three dimensional figures all show up in the ECE Board Exam, and you need more than just memorized formulas to handle them well.

This is Part 1 of the Solid Geometry MCQ Series on Pinoybix, compiled to give electronics engineering students a focused and practical way to review this topic before exam day. The questions here come from past ECE Board Exam problems, engineering mathematics textbooks, academic journals, and other references that have been useful to reviewees over the years.

Go through each item with full attention. Solid geometry problems often require you to visualize the figure before you can even set up the solution, so take the time to understand what each question is actually asking. Rushing through this one will cost you.

If this is the beginning of your review on this topic, you are in the right place. Work through every problem, note what trips you up, and treat every wrong answer as something worth understanding. That is how you build the kind of readiness that holds up under actual exam conditions.

MCQ Topic Outline included in Mathematics Board Exam Syllabi

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

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each question.

Problem 1: ME Board October 1991

A circular piece of 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°

Problem 2: CE Board November 1994

What is the area in sq. me 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 m²

B. 565.5 m²

C. 665.5 m²

D. 656.5 m²

Problem 3: CE Board May 1995

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

Problem 4: CE Board November 1996

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%

Problem 5: ECE Board November 1996

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%

Problem 6: ECE Board November 1992

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

A. 5%

B. 10%

C. 21%

D. 33%

Problem 7: ECE Board November 1992

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

A. 5%

B. 10%

C. 21%

D. 33%

Problem 8: EE Board October 1991

How many times does the volume of a sphere increases if the radius is doubled?

A. 4 times

B. 2 times

C. 6 times

D. 8 times

Problem 9: CE Board May 1997

A circular 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

Problem 10: CE Board November 1997

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

A. 12367.2 cm³

B. 13232.6 cm³

C. 13503.4 cm³

D. 14682.5 cm³

Problem 11: CE Board May 1998

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 cm³

B. 6622.44 cm³

C. 7710.82 cm³

D. 8866.44 cm³

Problem 12: CE Board November 1996

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 (in cm³) of its content.

A. 188.40

B. 298.40

C. 381.70

D. 412.60

Problem 13: CE Board May 1995

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

A. 2x

B. 3x

C. 3.317x

D. 3.162x

Problem 14: CE Board November 1995

The ratio of the volume to the lateral area of a right circular cone is 2:1. If the altitude is 15 cm, what is the ratio of the slant height to the radius?

A. 5:6

B. 5:4

C. 5:3

D. 5:2

Problem 15: CE Board November 1994

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

Problem 16: CE Board November 1995

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

Problem 17: EE Board April 1992

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 cm³

B. 3180.87 cm³

C. 3108.87 cm³

D. 3081.87 cm³

Problem 18: EE Board April 1993

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 m³

B. 520,500 m³

C. 540,600 m³

D. 534,200 m³

Problem 19: ME Board April 1996

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. and 5.5 ft. respectively.

A. 413 ft³

B. 311 ft³

C. 313 ft³

D. 391 ft³

Problem 20: CE Board November 1995

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

Problem 21: CE Board May 1996

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 meters.

A. 4.00

B. 3.75

C. 3.50

D. 3.25

Problem 22: CE Board November 1997

The bases of a right prism is a hexagon 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 cm³

B. 2211.7 cm³

C. 1212.5 cm³

D. 1122.4 cm³

Problem 23: EE Board April 1996

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 of 6 ft and a height of 10 ft, the smaller tank has a diameter of 6 ft and a height of 8 feet. Neglect the volume of water in the pipeline.

A. 200^1/3

B. 50^1/3

C. 25^1/3

D. 50^1/4

Problem 24:

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

Problem 25:

A regular octahedron has an edge of 2 m. Find its volume (in m³).

A. 3.77

B. 1.88

C. 3.22

D. 2.44

Problem 26: CE Board May 1996

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

Problem 27: CE Board November 1996

The volume of water in a spherical tank having a diameter of 4 m is 5.236 m³. Determine the depth of the water in the tank.

A. 1.0

B. 1.2

C. 1.4

D. 1.8

Problem 28:

An ice cream cone is filled with ice cream and 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 cubic 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

Problem 29: ME Board April 1997

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 in³

B. 2.5 in³

C. 3.8 in³

D. 4.2 in³

Problem 30: CE Board May 1997

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 centimeters inside the shell is not occupied by the block?

A. 2714.56

B. 3714.65

C. 4713.56

D. 4613.74

31. If the edge of a cube is doubled, which of the following is incorrect?

A. The lateral area will be quadrupled

B. The volume is increased 8 times

C. The diagonal is doubled

D. The weight is doubled

32. The volume of a cube is reduced by how much if all sides are halved?

A. 1/8

B. 5/8

C. 6/8

D. 7/8

33. Find the volume of the sphere whose circumference of a great circle is 18π.

A. 3984.43

B. 3053.63

C. 3291.68

D. 3643.03

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

A. 67%

B. 69%

C. 63%

D. 65%

35. Find the approximate change in the volume of a cube of side x inches caused by increasing its side by 1%.

A. 0.3x³ cu. in.

B. 0.1x³ cu. in.

C. 0.02x³ cu. in.

D. 0.03x³ cu. in.

36. A rectangular bin 4 feet long, 3 feet wide, and 2 feet high is solidly packed with bricks whose dimensions are 8 in. by 4 in. by 2 in. The number of bricks in the bin is:

A. 68

B. 386

C. 648

D. 956

37. Find the total surface area of a cube of side 6 cm.

A. 214 sq. cm.

B. 216 sq. cm.

C. 226 sq. cm.

D. 236 sq. cm.

38. The space diagonal of a cube is 4√3 m. Find its volume.

A. 16 cubic meters

B. 48 cubic meters

C. 64 cubic meters

D. 86 cubic meters

39. A reservoir is shaped like a square prism. If the area of its base is 225 sq. cm, how many liters of water will it hold if its length is 1.5 meters?

A. 3.375

B. 3375

C. 33.75

D. 3375

40. Find the angle formed by the intersection of a face diagonal to the diagonal of a cube drawn from the same vertex.

A. 35.26°

B. 32.56°

C. 33.69°

D. 42.23°

41. The space diagonal of a cube (the diagonal joining two non-coplanar vertices) is 6 m. The total surface area of the cube is:

A. 60

B. 66

C. 72

D. 78

42. The base edge of a regular hexagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm.

A. 1563.45 cm³

B. 1058.45 cm³

C. 1896.37 cm³

D. 1122.37 cm³

43. The base edge of a regular pentagonal prism is 6 cm and its bases are 12 cm apart. Find its volume in cu. cm.

A. 743.22 cm³

B. 786.89 cm³

C. 567.45 cm³

D. 842.12 cm³

44. The base of a right prism is a hexagon with one side 6 cm long. If the volume of the prism is 450 cc, how far apart are the bases?

A. 5.74 cm

B. 3.56 cm

C. 4.11 cm

D. 4.81 cm

45. A trough has an open top 0.30 m by 6 m and closed vertical ends which are equilateral triangles 30 cm on each side. It is filled with water to half its depth. Find the volume of the water in cubic meters.

A. 0.058

B. 0.046

C. 0.037

D. 0.065

46. Determine the volume of a right truncated prism with the following dimensions: Let the corner of the triangular base be defined by A, B, and C. the length AB = 10 feet, BC = 9 feet and CA = 12 feet. The sides at A, B and C are perpendicular to the triangular base and have the height of 8.6 feet, 7.1 feet, and 5.5 feet, respectively.

A. 413 ft³

B. 311 ft³

C. 313 ft³

D. 391 ft³

47. The volume of a regular tetrahedron of side 5 cm is:

A. 13.72 cu. cm

B. 14.73 cu. cm

C. 15.63 cu. cm

D. 17.82 cu. cm

48. A regular hexagonal pyramid whose base perimeter is 60 cm has an altitude of 30 cm, the volume of the pyramid is:

A. 2958 cu. cm.

B. 2598 cu. cm.

C. 2859 cu. cm.

D. 2589 cu. cm.

49. A frustum of a pyramid has an upper base 100 m by 10 m and a lower base of 80 m by 8 m. if the altitude of the frustum is 5 m, find its volume.

A. 4567.67 cu. m.

B. 3873.33 cu. m.

C. 4066.67 cu. m.

D. 2345.98 cu. m.

50. The altitude of the frustum of a regular rectangular pyramid is 5 m the volume is 140 cu. m. and the upper base is 3 m by 4 m. What are the dimensions of the lower base in m?

A. 9 x 10

B. 6 x 8

C. 4.5 x 6

D. 7.50 x 10

Online Questions and Answers in Solid Geometry Series

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

Online Questions and Answers in Analytic Geometry: Points, Lines and Circles Series

Mathematics Board Examination Mastery | Math Engineering Pre-Board