MOCK FINALS
SOLIMEN QUESTIONS
1. A 8 cm chord in a circle is bisected by a perpendicular bisector, resulting in a 2 cm length from
one end of the bisector to the intersection. Find the radius of the circle.
a.
b. √
c.
d.
√
2. A cone and a sphere have the same volume. Find the ratio of the height of the cone with respect to its
base radius if the radius of the sphere is twice the radius of the base of the cone.
a. 4
b. 8
c. 16
d. 32
3. ABCD is a parallelogram whose diagonals have lengths of 10 cm and 5 cm and an angle of 35o
between them. Find the height of the parallelogram that is perpendicular to the shortest side.
a. 4.37 cm
b. 3.49 cm
c. 6.08 cm
d. 7.62 cm
4. Find the volume of a regular pentagonal pyramid whose base side is 7 cm and slant height is 8 cm.
a. 305.27 cm3
b. 164.35 cm3
c. 221.52 cm3
d. 493.05 cm3
5. A plane is used to divide the sphere of radius 6 in. into two parts. What should be the distance of the
plane from the center of the sphere if the smaller part is 1/3 of the total volume of the sphere?
a. 1.36 in.
b. 4.64 in.
c. 2 in.
d. 4 in.
6. Three circles are externally tangent to each other. If each circle has a diameter of 8 cm, find the area
bounded enclosed by the tangency of three circles.
a. 43.83 cm2
b. 10.32 cm2
c. 2.58 cm2
d. 10.96 cm2
7. A sector is to be cut from a circle of radius 5 cm. If a right circular cone is to be made from the sector,
what should be the minimum angle of the sector such that the cone can stand at a minimum height of 4
cm?
a. 54o
b. 108o
c. 162o
d. 216o
8. A rectangular parallelepiped has sides of 6, 8, and 10 in. Find the area of the triangle as shown:
a. 60 cm2
b. 48 cm2
c. 55.46 cm2
d. 38.64 cm2
9. An transparent can of radius 7 in and height 15 in contains water which is ¼ its volume. A child is
curious as to what would the water height be if he position the can horizontally instead of standing
vertically. If the child measures this height using a ruler, what height will he obtain?
a. 4.88 cm
b. 2.12 cm
c. 3.22 cm
d. 3.78 cm
10. A water tank is to be made which should consist of a cylindrical section and two hemispherical
sections found at the ends of cylindrical section. The total height of the tank should be 15 m and the
diameter of the hemispherical section is 8 m. What will be the cost of the tank if a metal sheet is to be
used to make it, where each 1 m2 of metal sheet costs P 50?
a. P 18850
b. P 77912
c. P 30998
d. P 28903
11. In number 10, what will be the maximum volume of water that can be stored inside the tank?
a. 1022.06 m3
b. 578.05 m3
c. 376.99 m3
d. 619.94 m3
12. A circle is inscribed inside a regular hexagon. A bigger circle is circumscribed about the hexagon.
If the circumference of the bigger circle is 44π cm2, what the ration of the area of the small circle
to that of the bigger circle?
(a) 4:5
(b) 2:5
(c) 3:4
(d)1:3
The figure below consists of a semicircle and a quarter circle inside a square. Find the area of the
shaded region in the figure if the length of the side of the square is 14 inches. (Express your
answer in terms of π).
(a)
(b)
(c)
(d)
13. An isosceles triangle has a base of 12cm and a height of 20cm. A line parallel to the base is
drawn so that the area of the resulting trapezoid is half the area of the original triangle. How far
from the base is the parallel line drawn? (Express your answer to the nearest hundredths.)
(a) 14.14 cm
(b) 5.86 cm
(c) 13.33 cm
(d) 8.49 cm
14. In the sides of a regular pentagon are extended to form a 5-pointed star. The points of the stars
are connected to form a bigger pentagon. If the sides of smaller pentagon measure 5cm, what is
the area inside the bigger pentagon but outside the smaller pentagon?
(a) 30.69 cm2
(b) 37.35 cm2
(c) 44.13 cm2
(d) 32.37 cm2
15. A replica of a pencil as made up of wood. The solid is made by connecting a hemisphere on one
end of a cylinder and a cone of the other end. The radius of the cylinder is 4 inches and its length
is 6 inches. If the whole solid is 13 inches long, how much wood is needed to make such replica?
(a) 157.33 π in3
(b) 154.67 π in3
(c)152.01π in3
(d) 149.35π in3
16. A rectangular prism with dimensions 15 cm by 20 cm by 25 cm is made up of iron. Two
cylindrical holes are to be drilled from the solid. Both cylinders have radius 5cm. One is 5cm
deep while the other is 10cm deep. The holes filled with lead. If the density of iron is 7.87g/cm 3
and the density of lead is 11.34g/cm3, what is the total weight of the metal prism in kilograms?
(a) 64.92kg
(b) 71.36 kg
(c) 69.21 kg
(d) 63.11 kg
17. A traffic cone is in the shape of a conical frustum. The two radii measure 4 inches and 10 inches,
and the cone is 2 feet tall. If the cone is to be painted, how much area is needed to be covered?
In this instance, assume that the base will not be painted, the thickness of the base and the cone
is negligible, and the top of cone is open.
(a) 1078.98 in2
(b) 1087.84 in2
(c) 1063.79 in2
(d) 1094.46 in2
18. What is the area of triangle with sides 14.5 cm, 22.3 cm, and 17.7 cm?
a. 128.2 cm3
b. 153.3 cm2
c. 1,592 cm2
d. None of the above
19. What is the edge length of a regular hexagon inscribed in a circle with an area of 16π
cm2?
a. 4 cm
b. 4.5 cm
c. 5 cm
d. 5.5 cm
20. A wooden block in the shape of an octagonal pyramid has a base edge of 3 cm and an
altitude of 10 cm. How much wood was needed to make the block?
a. 74.6 cm3
b. 144.8 cm3
c. 434.4 cm3
d. 868.8 cm2
21. A pencil is to be placed inside a rectangular box with a length of 6 inches, a width of 4
inches, and a height of 3 inches. What is the length of the longest pencil that can fit in the
box?
a. 5.1 inches
b. 6.0 inches
c. 7.8 inches
d. 8.5 inches
22. A can of juice has a circular base with diameter of 5 cm. What is the height of the can if
it is filled with 250 mL of juice?
a. 11.4 cm
b. 12.7 cm
c. 12.9 cm
d. 13.6 cm
23. What is the altitude of a right circular cone which was obtained from a sector of a circle
with a central angle of 120° and a radius of 12 cm?
a. 11.3 cm
b. 11.9 cm
c. 12.4 cm
d. None of the above
24. A water trough in the shape of a triangular prism is to be filled with 100 cubic inches of
water. How deep is the water in the trough if the trough is 16 inches long, 9 inches in
altitude, and 1.2 feet wide across the top?
a. 1.2 inches
b. 3.7 inches
c. 5.5 inches
d. 6.5 inches
25. How much paint is needed to completely cover half a Styrofoam ball with a diameter of
5.7 inches?
a. 51.0 in2
b. 76.6 in2
c. 102.1 in2
d. 306.2 in2
For numbers 26 – 28
The tin which requires at least sheet of tins for a given volume has its diameter and altitude equal. The
available tin sheet is 200 sq. Dm, disregarding waste, if each will hold a liter (1L = 1000cm3).
26. What is the radius of the can
a. 10.84 cm
b. 5.42 cm
c. 35.68 cm
d. 17.84 cm
27. What is the total surface area of each can?
a. 169.25 cm2
b. 369.15 cm2
c. 533.53 cm2
d. 535.35 cm2
28. How many tin cans can be mase from the available tin sheet?
a. 118 cans
b. 54 cans
c. 36 cans
d. 37 cans
29. A spherical wedge of a sphere of radius 12 inches has an angle which measures 90 degrees. Find
the volume of the wedge
a. 288pi in3
b. 576pi in3
c. 462pi in3
d. 325pi in3
30. Find the volume of the truncated right square prism with side 5 m and whose lateral edges are
3, 5m, 7m and 9m, respectively.
a. 200m3
b. 175m3
c. 225m3
d. 150m3
Answers
1.C
11. D
21. C
2. D
12. C
22. B
3. A
13. B
23. A
4. B
14. A
24. C
5. A
15. B
25. B
6. C
16. D
26. B
7. D
17. C
27. C
8. C
18. D
28. C
9. B
19. A
29. B
10. A
20. B
30. D