November 2022 Eval Exam 2 Review Innovations

1. In triangle ABC, c = 30, a = 36 and b = 18. Find the radius of the circle
tangent to the side c and escribe outside the triangle.
A. 22.45 C. 18.17
B. 20.12 D. 23.65

2. If x + y = 900, what is the value of (sin x tan y)/(sin y tan x)?

A. sin x C. csc x
B. tan x D. cot x

3. Two sides of a triangle are 50m and 60m long. The angle included between
these sides is 30°. What is the interior angle opposite the longest side?
A. 83.71° C. 85.38°
B. 92.74° D. 93.75°

4. Triangle ABC has side AB = 160 cm, BC = 190 cm, and CA = 190 cm. Point D is
along side AB and AD = 100 cm. Point E is along side CA. Determine the length
of AE if the area of triangle ADE is 3/5 the area of triangle ABC.
A. 182.4 cm C. 185.7 cm
B. 176.3 cm D. 175.4 cm

5. A flagpole 3m high stands at the top of a pedestal 2m high located at one side
of a pathway. At the opposite side of the pathway directly facing the flagpole,
the flagpole subtends the same angle as the pedestal. What is the width of the
pathway?
A. 5.29 m C. 4.47 m
B. 6.12 m D. 5.39 m

6. Two runners A and B started from the same point on a circular track 20m in
radius and ran at the same rate of 2 m/s ; A running towards the center and B
along the circumference. How far apart are they after 8 seconds?
A. 17.45 m C. 15.57 m
B. 14.75 m D. 16.12 m

7. A rectangular tank 6m wide 12m long and 18m high is 2/3 full of water. If 120m3
of water is added, how much (in percent) is the tank filled with water?
A. 75.93% C. 66.67%
B. 79.53% D. 76.67%

8. A circle whose area is 452 cm2 is cut into two segments by a chord whose
distance from the center of the circle is 6 cm. Find the area of the larger
segment in cm2.
A. 311 C. 389
B. 324 D. 364

9. A right prism has a base in the shape of regular octagon inscribed in a square
10 cm by 10 cm. If its altitude of 15 cm, find its volume in cubic centimeter.
A. 1250.12 C. 1302.56
B. 1242.64 D. 1230.45

10. The lateral area of a right circular cone is 386 m2. If its diameter is one-
half its altitude, determine its altitude in meters.
A. 20.5 C. 23.9
B. 21.4 D. 22.5

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November 2022 Eval Exam 2 Review Innovations

11. If the one side of a rectangle is increased by 25%, what is the effect on the
other side to maintain the same area?
A. decreased by 80% C. increased by 80%
B. decreased by 20% D. increased by 20%

12. A square of perimeter 20 is inscribed in a square of perimeter 28. What is the

greatest distance between a vertex of the inner square and a vertex of the
outer square?
A. √58 C. √65
B. 8 D. 5√3

13. How many different value(s) of 𝑥 from 0° to 180° satisfies the equation
(𝟐 𝐬𝐢𝐧 𝒙 − 𝟏)(𝐜𝐨𝐬 𝒙 + 𝟏) = 𝟎?
A. 1 C. 3
B. 2 D. 0

14. A goat is tied to a corner of a 30 ft by 35 ft building. If the rope is 40 ft

long and the goat can reach 1 ft farther than the rope length, what is the
maximum area the goat can cover?
A. 5281 ft2 C. 3961 ft2
B. 4084 ft 2 D. 4970 ft2

15. Two ships are sailing in the sea on opposite sides of a lighthouse. The angles
of elevation of the top of the lighthouse as observed from the ships are 34°
and 43°. If the lighthouse is 90 meters high, then the distance between the
ships is _______?
A. 225 m C. 220 m
B. 215 m D. 230 m

16. A mercury barometer at the base of a mountain reads 736 mm. At the same time,
another barometer at the top of the mountain reads 590 mm. Assuming air weighs
12 N/m3, the height of the mountain is nearest to:
A. 1849 m C. 1623 m
B. 2708 m D. 2017 m

17. An open tank contains a liquid 5 m deep of unit weight 7 kN/m 3. Water, of
unit weight 9.81 kN/m3, is poured over the liquid and the total depth of
both liquids is 8 m. Obtain the gage pressure in kPa at the point 6 m from
the surface.
A. 44.8 C. 50.4
B. 64.4 D. 29.4

18. A barometer reads 76 cm Hg and a pressure gage attached to a tank reads 38

cm of Hg. Determine the absolute pressure (kPa) in the tank.
A. 152 C. 148
B. 164 D. 170

19. A capillary tube of a uniform bore is dipped vertically in water which rises
7 cm in the tube. Find the radius of the capillary, in mm, if the surface
tension is 0.07 N/m.
A. 0.4 C. 0.6
B. 0.2 D. 0.8

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November 2022 Eval Exam 2 Review Innovations

20. Two pipes on the same elevation convey water and oil of specific gravity
0.88 respectively. They are connected by a U-tube manometer with the
manometric liquid having a specific gravity of 1.25. If the manometric
liquid in the limb connecting the water pipe is 2 m higher than the other
find the pressure difference in two pipes, in kPa, if h = 3 m.
A. 11.1 C. 12.1
B. 9.9 D. 10.8

21. A 120 mm square piece of wood (sg = 0.75) is 1.5 m long. How many Newtons
of lead weighing 110 kN/m3 must be fastened at one end of the stick so that
it will float upright with 0.3 m out of water.
A. 15.47 C. 12.95
B. 11.63 D. 13.88

22. A stone weighs 100 N in air, and when immersed in water it weighs 60 N.
Compute the specific gravity of the stone.
A. 2.5 C. 3.4
B. 1.9 D. 2.9

23. A spherical balloon 9.5 m in diameter weighs 1250 N. It is filled with

helium weighing 1.65 N/m3. Determine the maximum load (N) the balloon can
lift. γair = 12 N/m3.
A. 3671 C. 3519
B. 3408 D. 3396

24. A rectangular plate 1 m wide by 2.4 m long is vertically submerged in water,

the shorter edge 2 m. below and parallel to the water surface. Evaluate
how far in meters, below the centroid of the plate is the resultant
horizontal force acting on each side of it.
A. 0.15 C. 0.36
B. 0.24 D. 0.40

Situation 1. A 3.5-m square plate is immersed in water in a vertical position

such that the two edges of the square is horizontal. The immersion is
such that the center of pressure in the plate is 12 cm from the center of
gravity.

25. How far below the water surface should the upper plate be submerged?
A. 8.63 C. 6.76
B. 4.16 D. 5.62

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November 2022 Eval Exam 2 Review Innovations

26. What is the distance of the center of pressure from the water surface?
A. 8.63 C. 6.76
B. 4.16 D. 5.62

27. Determine the hydrostatic force in kN acting on the plate at this position.
A. 1165 C. 1549
B. 1022 D. 1287

Situation 2. A vertical triangular plate with base horizontal and 3.6 m high
is submerged in water. The distance between the center of gravity and the
center of pressure is 20 cm.

28. How deep is the water from the tip of the triangle, in meter(s)?
A. 1.2 C. 1.8
B. 3.6 D. 0.6

29. If the total force acting on one side of the triangle is 79.46 kN, find the
base width of the triangle, in meter(s)?
A. 1.25 C. 2.50
B. 3.75 D. 7.50

30. Find the depth of water to the center of pressure, in meter(s)?

A. 4.4 C. 6.2
B. 3.8 D. 3.2

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