Past Board Exam Problems B. 6622.44 cm3 A. 3.

50
C. 7710.82 cm3 B. 3.75
in Solid Geometry D. 8866.44 cm3 C. 4.00
D. 4.25
7. CE Board Exam November 1996
1. CE Board Exam November 1994 A conical vessel has a height of 24 13. CE Board Exam May 1996
What is the area in sq m of the zone cm and a base diameter of 12 cm. It A circular cylinder is circumscribed
of a spherical segment having a holds water to a depth of 18 cm about a right prism having a square
volume of 1470.265 cm m if the above its vertex. Find the volume (in base one meter on an edge. The
diameter of the sphere is 30 m? cm3) of its content. volume of the cylinder is 6.283 cu. m.
A. 465.5 m2 A. 188.40 Find its altitude in meters.
B. 565.5 m2 B. 298.40 A. 4.00
C. 665.5 m2 C. 381.70 B. 3.75
D. 656.5 m2 D. 412.60 C. 3.50
D. 3.25
2. CE Board Exam May 1995 8. CE Board Exam May 1995
A sphere having a diameter of 30 cm What is the height of a right circular 14. CE Board Exam November 1997
is cut into 2 segments. The altitude of The bases of a right prism are a
the first segment is 6 cm. What is the cone having a slant height of 10x
and a base diameter of 2x? hexagon with one of each side equal
ratio of the area of the second to that

m
A. 2x to 6 cm. The bases are 12 cm apart.

er as
of the first? What is the volume of the right
A. 4:1 B. 3x
prism?

co
B. 3:1 C. 3.317x
A. 1211.6 cm3

eH w
C. 2:1 D. 3.162x
B. 2211.7 cm3
D. 3:2 C. 1212.5 cm3

o.
9. CE Board Exam November 1995
The ratio of the volume to the lateral D. 1122.4 cm3
3. CE Board Exam November 1996
rs e
If the edge of a cube is increased by area of a right circular cone is 2:1. If
ou urc
the altitude is 15 cm, what is the ratio 15. CE Board Exam May 1996
30%, by how much is the surface A mixture compound of equal parts of
area increased? of the slant height to the radius?
A. 5:6 two liquids, one white and the other
A. 30% black, was placed in a hemispherical
B. 33% B. 5:4
bowl. The total depth of the two
o

C. 60% C. 5:3
D. 5:2 liquids is 6 inches. After standing for
aC s

D. 69% a short time, the mixtures separated,

vi y re

10. CE Board Exam November 1994 the white liquid settling below the
4. CE Board Exam May 1997 black. If the thickness of the segment
A circular cone having an altitude of 9 A regular triangular pyramid has an
altitude of 9 m and a volume if 187.06 of the black liquid is 2 inches, find the
m is divided into 2 segments having radius of the bowl in inches.
the same vertex. If the smaller cu. m. What is the base edge in
meters? A. 7.33
altitude is 6, find the ratio of the
ed d

A. 12 B. 7.53
volume of the small cone to the big C. 7.73
B. 13
ar stu

cone. D. 7.93
A. 0.186 C. 14
B. 0.296 D. 15
16. CE Board Exam November 1996
C. 0.386 The volume of water in a spherical
D. 0.486 11. CE Board Exam November 1995
tank having a diameter of 4 m is
sh is

The volume of the frustum of a

regular pyramid is 135 cu. m. The 5.236 m3. Determine the depth of the
5. CE Board Exam November 1997 water in the tank.
Th

Find the volume of a cone to be lower base is an equilateral triangle

with an edge of 9 m. The upper base A. 1.0
constructed from a sector having a B. 1.2
diameter of 72 cm and central angle is 8 m above the lower base. What is
the upper base edge in meters? C. 1.4
of 210°. D. 1.8
A. 12367.2 cm2 A. 2
B. 13232.6 cm2 B. 3
C. 4 17. CE Board Exam May 1997
C. 13503.4 cm2 The corners of a cubical block
D. 14682.5 cm2 D. 5
touched the closed spherical shell
12. CE Board Exam November 1995 that encloses it. If the volume of the
6. CE Board Exam May 1998 box is 2744 cm3, what volume in cm3
Find the volume of a cone to be A circular cylinder with a volume of
6.5 cu. m us circumscribed about a inside the shell is not occupied by the
constructed from a sector having a block?
diameter of 72 cm and a central right prism whose base is an
equilateral triangle if side 1.25 m. A. 2714.56
angle of 150°. B. 3714.65
A. 5533.32 cm3 What is the altitude of the cylinder in
meters? C. 4713.53

https://www.coursehero.com/file/23984067/Past-Board-Exam-Problems-in-Solid-Geometrypdf/
 D. 4613.74 diameter when the surface area D. 14.33
increases by 21%?
18. EE Board Exam October 1991 A. 5% 30. ECE April 2000, November 1999
How many times do the volume of a B. 10% A regular hexagon pyramid has a
sphere increases if the radius is C. 21% slant height of 4 cm and the length of
doubled? D. 33% each side of the base is 6 cm. Find
A. 4 times the lateral area.
B. 2 times 24. ECE Board Exam November 1992 A. 62 cm2
C. 6 times Given a sphere of diameter d, what is B. 52 cm2
D. 8 times the percentage increase in its volume C. 72 cm2
when the surface area increases by D. 82 cm2
19. EE Board Exam April 1992 21%?
What is the volume of a frustum of a A. 5% 31. ECE November 2000
cone whose upper base is 15 cm in B. 10% The lateral area of the right circular
diameter and lower base 10 cm in C. 21% water tank is 92 cm2 and its volume is
diameter with an altitude of 25 cm? D. 33% 342 cm3. Determine the radius.
A. 3018.87 cm3 A. 5.56 cm
B. 3180.87 cm3 25. ECE November 1995 B. 6.05 cm
C. 3108.87 cm3 Each side of a cube is increased by C. 7.28 cm

m
D. 3081.87 cm3 10%. By what percent is the volume D. 7.43 cm

er as
of the cube increased?
20. EE Board Exam April 1993 A. 33.1% 32. ECE November 2000

co
In a portion of an electrical railway B. 3.31% A cone and cylinder have the same

eH w
cutting, the areas of cross section C. 0.031% height and the same volume Find the
taken every 50 m are 2556, 2619, D. 13.31% ratio of the radius of the cone to the

o.
2700, 2610 and 2484 sq m. Find its radius of the cylinder?
volume.
rs e 26. ECE November 1996 A. 0.577
ou urc
A. 522,600 m3 A reservoir is shaped like a square B. 1.732
B. 520,500 m3 prism. If the area of its base is 225 C. 0.866
C. 540,600 m3 square centimeters, how many liters D. 1.414
D. 534,200 m3 will it hold?
A. 337.5 33. ECE April 2001
o

21. EE Board Exam April 1996 B. 3.375 It is desired that the volume of the
aC s

Two vertical conical tanks are joined C. 3375 sphere be tripled. By how many times
vi y re

at the vertices by a pipe. Initially the D. 33.75 will the radius increased?
bigger tank is full of water. The pipe A. 21/2
valve is open to allow the water to 27. ECE November 1999 B. 31/3
flow to the smaller tank until it is full. A metal washer 1–inch in diameter is C. 31/2
At this moment, how deep is the pierced by a ½-inch hole. What is the D. 33
ed d

water in the bigger tank? The bigger volume of the washer if it is 1/8-inch
tank has a diameter of 6 ft and a thick? 34. ECE November 2001
ar stu

height of 10 ft, the smaller tank has a A. 0.074 If the lateral area of a right circular
diameter of 6 ft and a height of 8 ft. B. 0.047 cylinder is 68 and is volume is 220,
Neglect the volume of the water in C. 0.028 find its radius.
the pipeline. D. 0.082 A. 4
B. 3
sh is

A. 3 200 answer
3
28. ECE November 1999 C. 5
B. 50 Find the approximate change in the D. 2
Th

3
C. 25 volume of a cube of side “x” inches
4 caused by increasing its side by 1%. 35. ECE November 2001
D. 50
A. 0.30 x2 in2 Find the increase in volume of a
B. 0.02x2 in2 spherical balloon when the radius is
22. ECE Board Exam April 1995 C. 0.010x2 in2 increased from 2 to 3 inches.
Each side of a cube is increased by D. 0.03x2 in2 A. 74.12 cu. in
1%. By what percent is the volume of B. 74.59 cu. In
the cube increased? 29. ECE November 1999 C. 75.99 cu. in
A. 1.21% What is the distance between two D. 79.59 cu. in
B. 2.8% vertices of a cube which are farthest
C. 3.03% from each other, if an edge measures 36. ECE November 2001
D. 3.5% 8 cm? A pyramid whose altitude is 5 ft
A. 13.86 weight 800 lbs. At what distance from
23. ECE Board Exam November 1992 B. 11.32 its vertex must it be cut by a plane
Given a sphere of diameter d, what is C. 16.93
the percentage increase in its

https://www.coursehero.com/file/23984067/Past-Board-Exam-Problems-in-Solid-Geometrypdf/
 parallel to its base so that the two D. 1205 cm3 D. 154°
solids of equal weight will be formed?
A. 2.52 ft 43. ECE November 2005 49. ME Board Exam April 1997
B. 2.96 ft The total volume of two spheres is A cubical container that measures 2
C. 3.97 ft 100pi cubic units. The ratio of their inches on a side is tightly packed with
D. 4.96 ft areas is 4:9. What is the volume of 6 marbles and is filled with water. All
the smaller sphere in cubic units? 8 marbles are in contact with the
37. ECE November 2001 A. 75.85 walls of the container and the
The circumference of a great circle if B. 314.16 adjacent marbles. All of the marbles
a sphere is 18π. Find the volume of a C. 71.79 are of the same size. What is the
sphere. D. 242.36 volume of the water in the container?
A. 3023.6 A. 0.38 in3
B. 3043.6 44. ECE November 1996 B. 2.5 in3
C. 3033.6 Prisms are classified according to C. 3.8 in3
D. 3053.6 their D. 4.2 in3
A. diagonals
38. ECE November 2003, November B. sides 50. ME April 1998
1999 C. vertices The study of the properties of figures
The volume of two spheres is in the D. bases of three dimensions

m
ratio 27:343 and the sum of their radii A. physics

er as
is 10. Find the radius of the smaller 45. ECE November 1996 B. plane geometry
sphere. It is a polyhedron of which two faces C. solid geometry

co
A. 5 are equal polygons in parallel planes D. trigonometry

eH w
B. 4 and the other faces are
C. 3 parallelograms 51. ME April 1998

o.
D. 6 A. tetrahedron The volume of a circular cylinder is

rs e B. prism equal to the product of its base and

ou urc
39. ECE April 2003 C. frustum altitude
The area of one of the faces of an D. prismatoid A. postulate
icosahedron is 5 sq. m. What is the B. theorem
total surface area of the said solid? 46. ECE November 1996 C. corollary
A. 89.3 sq. m Polygons are classified according to D. axiom
o

B. 100 sq. m the number of

aC s

C. 97.3 sq. m A. vertices 52.

vi y re

D. 78.2 sq. m B. sides

C. diagonals A.
40. ECE November 2003 D. angles B.
A cube of ice is 64 cu. ft. The ice C.
melts until it becomes a cube, which 47. ME Board Exam April 1996 D.
ed d

is one-half of its original volume. Determine the volume of a right 53.

What is the length of the edge of the truncated prism with the following
ar stu

new cube? definitions. Let the corners of the A.

A. 7.31 ft triangular base be defined by A, B B.
B. 3.17 ft and C. The length of AB = 10 ft., BC C.
C. 1.73 ft = 9 ft., and CA = 12 ft. The sides A, B D.
D. 3.71 ft and C are perpendicular to the
sh is

triangular base and have a height of 54.

41. ECE April 2004 8.6 ft., 7.1 ft., and 5.5 ft., respectively.
Th

By how many percent will the volume A. 413 ft3 A.

of a cube increase if its edge is B. 311 ft3 B.
increase by 20%? C. 313 ft3 C.
A. 72.80 D. 391 ft3 D.
B. 17.28
C. 80.00 48. ME Board Exam October 1991
D. 1.728 A circular of cardboard with a
diameter of 1 m be made into a
42. ECE November 2005 conical hat 40 cm high by cutting a
What is the volume of a hexagonal sector off and joining the edges to
prism 15 cm high and with one of its form a cone. Determine the angle
sides equal to 6 cm? subtended by the sector removed.
A. 955 cm3 A. 144°
B. 1403 cm3 B. 148°
C. 810 cm3 C. 152°

https://www.coursehero.com/file/23984067/Past-Board-Exam-Problems-in-Solid-Geometrypdf/

Powered by TCPDF (www.tcpdf.org)