MULTIVECTOR REVIEW CENTER CO.
Unit M1, First Floor, CMFFI Building A, 813 Papa St. , Sampaloc, Manila
SUPPLEMENTARY PROBLEMS
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7.
Find the area of an isosceles triangle with a base of
19.2 in and base angles of 23°10’ each.
A. 39.4 in2
C. 41.6 in2
2
B. 40.5 in
D. 42.7 in2
A painter needs to find the area of the gable end of a
house. What is the area of the gable if it is a triangle
with two sides of 42.0 ft that meet at a 105° angle?
A. 850 ft2
C. 852 ft2
2
B. 851 ft
D. 853 ft2
Three circles with radii 3 cm, 5 cm, and 9 cm are
externally tangent. What is the area of the triangle
formed by joining their centers?
A. 47 cm2
C. 49 cm2
B. 48 cm2
D. 50 cm2
A rail road is to be laid-off in circular path. What should
be the radius if the track is to change direction by 30
degrees at distance of 157. 08 m ?
A. 200 m
C. 400 m
B. 300 m
D. 500 m
A goat is tied to an external corner of a rectangular
shed measuring 4 m by 6 m. If the goat’s rope is 8 m
long, what is the total area, in square meters, in which
the goat can graze?
A. 163.2 m2
C. 165.4 m2
2
B. 164.3 m
D. 166.6 m2
Find the area of a segment of a circle with a central
angle of 75 degrees and a radius of 5 inches.
A. 942. 34 in2
C. 944.36 in2
2
B. 943. 35 in
D. 945.37 in2
The area of the small segment of a circle with radius 6
m is 28 m2. Find the length of its chord.
A. 8.93 m
C. 10.95 m
B. 9.94 m
D. 11.96 m
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15.
Chords AB and AC are drawn on a circle of radius 10
inches. Find the angle between the chords if the arc
BAC is 28 inches long.
A. 160.430
C. 162.450
0
B. 161.44
D. 163.460
Find the angle in mills subtended by a line 10 yards
long at a distance of 5000 yards.
A. 1
C. 2.5
B. 2
D. 3
Two concentric cirles of radii 5 cm and 3 cm. Find the
length of the chord of the larger circle which touches
the smaller circle.
A. 2 cm
C. 4 cm
B. 3 cm
D. 5 cm
Two concentric circles have a chord running through
the outer one. The chord is the tangent of the inner
circle and is 14 cm. Find the area of the region outside
the inner circle but outside the outer circle.
A. 16π cm2
C. 36π cm2
2
B. 25π cm
D. 49π cm2
Given a triangle with sides 3 cm, 4 cm, and 5 cm. Find
the length of the median to the longest side.
A. 1.5 cm
C. 2.5 cm
B. 2 cm
D. 3 cm
Refer to the given in #12, find the length of the angle
bisector of the right angle.
A. 2.42 cm
C. 4.44 cm
B. 3.43 cm
D. 5.45 cm
Refer to the given in#12, find the length of the altitude
if the base is the longest side.
A. 2 cm
C. 12/5 cm
B. 11/5 cm
D. 13/5 cm
Refer to the given in #12, find the radius of the
circumscribing circle.
A. 1.5 cm
C. 2.5 cm
B. 2 cm
D. 3 cm
16. Refer to the given in #12, find the radius of the
inscribed circle.
A. 1 cm
C. 3 cm
B. 2 cm
D. 4 cm
17. The chords AB and CD intersect at the point E
within the circle. The chord CD has the measure of
10 units. segments CE and AE have the measures
of 6 and 4 units. Find the measure of the chord AB.
A. 10 units
C. 12 units
B. 11 units
D. 13 units
18. A road is tangent to a circular lake. Along the road and
12 miles from the point of tangency, another road
opens towards the lake. From the intersection of the
two roads to the periphery of the lake, the length of
the new road is 11 miles. If the new road will be
prolonged across the lake, find the length of the bridge
to be constructed.
A. 0.07 miles
C. 2.09 miles
B. 1.08 miles
D. 3.10 miles
19. A hexagon is inscribed in a circle with radius of 10 cm.
Find the area of the hexagon.
A. 200 cm2
C. 300 cm2
B. 250 cm2
D. 400 cm2
20. Refer to the given in #19, find the length of the
apothem.
A. 8.66 cm
C. 10.88 cm
B. 9.77 cm
D. 12 cm
21. Refer to the given in #19, find the length of the side.
A. 8 cm
C. 10 cm
B. 9 cm
D. 11 cm
22. Refer to the given in #19, find the number of
diagonals.
A. 8
C. 10
B. 9
D. 11
23. Refer to the given in #19, find the sum of interior
angles.
A. 5400
C. 9000
MULTIVECTOR REVIEW CENTER CO.
Unit M1, First Floor, CMFFI Building A, 813 Papa St. , Sampaloc, Manila
24.
25.
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31.
B. 7200
D. 10800
Refer to the given in #19, find each of interior angle.
A. 600
C. 1200
0
B. 90
D. 1500
Refer to the given in #19, find each of exterior angle.
A. 600
C. 1200
0
B. 90
D. 1500
The area of a regular polygon inscribed in a circle is to
the area of a regular circumscribed polygon have the
same number of sides is 3:4. How many sides are
there in each polygon.
A. 4
C. 6
B. 5
D. 7
Find the area enclosed by a regular polygon pentagram
inscribed in a circle with radius 10 cm.
A. 112.3 cm2
C. 114.5 cm2
2
B. 113.4 cm
D. 115.6 cm2
Determine the area of a regular 6-star polygon if the
inner regular hexagon has 10 cm sides.
A. 510 cm2
C. 530 cm2
2
B. 520 cm
D. 540 cm2
The parallelogram ABCD with angle A = 5x + 2 and
angle C = 6x – 4. Find angle A.
A. 300
C. 320
B. 310
D. 330
A trapezoid 6 cm in altitude have bases of 12 cm and
18 cm respectively. If it is divided into two parts by
parallel line to the bases such that the ratio of the
areas of two parts formed 2:3. Compute the length of
dividing line.
A. 14.7 cm
C. 16.9 cm
B. 15.8 cm
D. 18 cm
A quadrilateral is inscribed in a circle in such a way that
one of the sides is the diameter of the circle. If the
three other sides are 1 cm, 2 cm, and 3 cm
respectively. Find the area enclosed by the
quadrilateral.
32.
33.
34.
35.
36.
37.
38.
A. 2.91 cm2
C. 4.93 cm2
2
B. 3.92 cm
D. 5.94 cm2
A trough having an equilateral triangle end section has
sides equal to 0.30 m and 6 m long. Find the volume of
water in the container if the depth of water is on half
the depth of trough?
A. 0.058 m3
C. 0.070 m3
3
B. 0.069 m
D. 0.081 m3
A swimming pool has a plan 18 ft by 40 ft and a
sloping bottom which is 3 ft deep at one end and 12 ft
at the other end. If the water from a full cylindrical
reservoir 12 ft in diameter and 40 ft deep is emptied
into the pool, find the depth of water in the deeper
end.
A. 9.77 ft
C. 11.79 ft
B. 10.78 ft
D. 12.80 ft
A conical vessel has a height of 16 cm and a base of 8
cm. Find the amount of material used.
A. 205 cm2
C. 207 cm2
2
B. 206 cm
D. 208 cm2
Refer to the given in #34, find the volume of the water
if it is 12 cm above its vertex.
A. 110 cm3
C. 112 cm3
B. 111 cm3
D. 113 cm3
Find the volume of the tetrahedron with edge 10 cm
long.
A. 117.85 cm3
C. 119.87 cm3
3
B. 118.86 cm
D. 120.88 cm3
Refer to the given in #36, find the total surface area.
A. 170.18 cm2
C. 172.20 cm2
2
B. 171.19 cm
D. 173.21 cm2
A frustum of a regular pyramid has a lower base of 10
cm by 10 cm and an upper base of 5 cm by 5 cm. It
has a lateral edge of 8 cm. Find the lateral surface
area.
A. 228 cm2
C. 230 cm2
2
B. 229 cm
D. 231 cm2
39. Refer to the given in #38, find the volume.
A. 114 cm3
C. 316 cm3
3
B. 215 cm
D. 417 cm3
40. Find the lateral area of the frustum of a cone with base
radii of 3 cm and 6 cm and height of 10 cm.
A. 295 cm2
C. 497 cm2
2
B. 396 cm
D. 598 cm2
41. Refer to the given in #40, find the volume.
A. 440 cm3
C. 660 cm3
3
B. 550 cm
C. 770 cm3
42. A cylinder of radius 3 in is cut through the center of the
base by plane making an angle of 45 degrees with the
base. Find the volume of cut off.
A. 15 in3
C. 17 in3
3
B. 16 in
D. 18 in3
43. Two cylinders with radii 20 cm each are made to cross
each other. Find the volume of the solid common
between the cylinders.
A. 42 667 cm3
C. 44 887 cm3
3
B. 43 777 cm
D. 45 997 cm3
44. A solid has a circular base of radius of 3 cm. Find the
volume of the solid if every planar section
perpendicular to a fixed diameter is an isosceles
triangle with height of 4 cm.
A. 53.22 cm3
C. 55.44 cm3
B. 54.33 cm3
D. 56.55 cm3
45. Given the sphere of radius 10 cm. Find its surface area
A. 300π cm2
C. 500π cm2
2
B. 400π cm
D. 600π cm2
46. Refer to the given in #45, Find the volume.
A. 3180 cm3
C. 5200 cm3
3
B. 4190 cm
D. 5210 cm3
47. Refer to the given in #45, find the area of the lune cut
out if the wedge angle is 450.
A. 20π cm2
C. 40π cm2
2
B. 30π cm
D. 50π cm2
MULTIVECTOR REVIEW CENTER CO.
Unit M1, First Floor, CMFFI Building A, 813 Papa St. , Sampaloc, Manila
48. Refer to the given in #45, find the volume of the
spherical wedge if the wedge angle is 450.
A. 523.6 cm3
C. 725.8 cm3
3
B. 624.7 cm
D. 826.9 cm3
49. Refer to the given in #45, find the area of the zone cut
out with the height of 3 cm.
A. 40π cm2
C. 60π cm2
2
B. 50π cm
D. 70π cm2
50. Refer to the given in #45, find the volume of the
spherical segment with height of 3 cm.
A. 100π cm3
C. 300π cm3
3
B. 200π cm
D. 400π cm3
51. Refer to the given in #45, find the area of spherical
triangle with 500, 800, and 1050 respectively.
A. 74 cm2
C. 96 cm2
2
B. 85 cm
D. 107 cm2
52. 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. 0.5 in3
C. 2.7 in3
B. 1.6 in3
D. 3.8 in3
53. Find the volume of solid generated by revolving an
ellipse with semi-major axis of 4 cm and semi-minor
axis of 3 cm about minor axis.
A. 64π cm3
C. 84π cm3
3
B. 72π cm
D. 96π cm3
54. Refer to the given in# 53, find the volume of solid
generated if it is revolve about major axis.
A. 48π cm3
C. 64π cm3
3
B. 56π cm
D. 72π cm3
55. Find the volume of paraboloid with radius of 3 cm and
height of 4 cm.
A. 9π cm3
C. 27π cm3
3
B. 18π cm
D. 36π cm3
56. What is the volume of the largest rectangular
parallelepiped which can be inscribed in the ellipsoid
x2/9 + y2/16 + z2/25 = 1?
A. 92.38 cm3
C. 204.4 cm3
3
B. 103.39 cm
D. 305.41 cm3
57. Two simlar polygons have sides of 4 cm and 8 cm. Find
the area of the smaller polygon if the area of larger
polygon is 64 cm2.
A. 12 cm2
C. 16 cm2
2
B. 14 cm
D. 20 cm2
58. A conical tank in upright position (vertex uppermost)
stored water of depth 2/3 that of the depth of the
tank. Calculate the ratio of the volume of water to that
of the tank.
A. 4/5
C. 26/27
B. 18/19
D. 2/3
59. The capacities of two hemispherical tanks are in the
ratio 64 : 125. If 4.8 kg of paint is required to paint the
outer surface of the smaller tank, the how many
kilograms of paint would be needed to paint the outer.
A. 6.4 kg
C. 8.6 kg
B. 7.5 kg
D. 9.7 kg
60. Find the ratio of the surface area of sphere with radius
r to its volume.
A. 2/r
C. 4/r
B. 3/r
D. 5/r