Civil Engineering Online Review

What is the volume of a spherical sector with angle of 60° in a sphere of radius 30cm?

A. 7576 cc
B. 7934 cc
C. 8212 cc
D. 7222 cc

Solution:

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A circle having an area of 1018 square centimeters is cut into two segments by a chord 8cn from the center. What is the ratio of the area of the smaller segment to the larger segment?

A. 0.125
B. 0.331
C. 0.293
D. 0.452

Solution:

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The perimeter of a triangle is 271cm. The interior angles measure 50°, 60°, and 70°, respectively. What is the length of the shortest side of the triangle?

A. 80.72 cm
B. 91.26 cm
C. 99.02 cm
D. 93.65 cm

Solution:

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The measure of the edge of a solid regular tetrahedron is 50cm. Find the distance of its center of gravity from its vertex.

A. 38.42 cm
B. 40.43 cm
C. 32.54 cm
D. 30.62 cm

Solution:

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Evaluate the following limit:

A. 0.7854
B. 1
C. 0.8745
D. 0.5784

Solution:

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Closed traverse has the following data:

1. What is the bearing of line DA?

A. S 76°33’ E
B. S 47°32’ E
C. S 86°59’ E
D. S 82°12’ E

2. What is the length of line DA?

A. 102.54 m
B. 83.33 m
C. 3,876.98 m
D. 96.19 m

3. What is the area of the lot?

A. 5,785.87 m²
B. 4,823.87 m²
C. 3,876.98 m²
D. 6,984.98 m²

Solution:

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The side slope of a road fill is 2H to 1V. The width of the roadbed (including shoulder and ditches) is 7m and the height of fill at the road center is 2.5m. The ground slopes-8% to the left.

1. What is the distance of the right slope stake from the road center?

A. 7.33 m
B. 8.32 m
C. 13.21 m
D. 10.12 m

2. What is the distance of the left slope stake from the road center?

A. 13.21 m
B. 10.12 m
C. 8.32 m
D. 7.33 m

3. What is the area of fill?

A. 35.98 m²
B. 25.32 m²
C. 30.95 m²
D. 32.87 m²

Solution:

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The purchase of a new car requires P100,000 down payment, P300,000 after two years, and P600,000 after five years. The interest rate is 18% compounded monthly.

1. What is the present worth of car?

A. P555,440.76
B. P645,982.43
C. P435,982.12
D. P782,123.23

2. What is the lump sum value of the car if paid after 5 years?

A. P1,123,985.34
B. P1,543,872.54
C. P1,357,063.84
D. P1,762,982.23

3. With a down payment of 100,000 and monthly interest of 1.5%, what is the monthly amortization of the car for 5 years?

A. P11,565.20
B. P12,546.87
C. P10,764.43
D. P9,765.34

Solution:

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A car with an initial velocity of 85 kph decelerates uniformly at 10m/min per second. Find the distance travelled after 30 seconds.

A. 853.3 m
B. 933.3 m
C. 783.3 m
D. 633.3 m

Solution:

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A ball fell from a height of 2.6m. the coefficient of restitution between the ball and the ground is 0.60. To what height  will the ball bounce?

A. 0.764 m
B. 0.936 m
C. 0.321 m
D. 1.56 m

Solution:

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A bullet is fired from a gun at an angle of 30° and muzzle velocity of 300 m/s. Determine the time for the bullet to fall to the ground.

A. 24.9 sec
B. 16.7 sec
C. 30.6 sec
D. 32.4 sec

Solution:

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Find the area bounded by the curve x²=16y and the x-axis from x=1 to x=3.

A. 1.342
B. 0.985
C. 0.542
D. 0.789

Solution:

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The circle x²+y²=36 is revolved about the line y=14, find the volume generated.

A. 9949
B. 9765
C. 10234
D. 11345

Solution:

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A searchlight 1.5 kilometers from a straight shore follows a car along the shore that moving at the speed of 10 kph. Find the rate of change of the angle of rotation of the searchlight when the car is 2km form a point on the shore nearest the searchlight.

A. 0.02 rad/min
B. 0.12 rad/min
C. 0.04 rad/min
D. 0.08 rad/min

Solution:

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A power plant located on one bank of a 900-m wide river is to supply electricity to a town on the opposite bank located 3 kilometers downstream from the power plant. The cost of wiring on water is $500 per meter and on land is $400 per meter. Find the most economical length of wire in meters.

A. 3,300
B. 3,100
C. 3,400
D. 3,200

Solution:

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Evaluate the following limit:

A. 0.5
B. 0.25
C. 0
D. 1

Solution:

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A parabola with vertex at the origin and vertical axis touches the point (3,4). Determine the latus rectum of the parabola.

A. 8
B. 4
C. 4.5
D. 2.25

Solution:

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What is the eccentricity of the curve 9x²-16y²-144x+224y+751=0?

A. 1.33
B. 1.67
C. 1.73
D. 1.54

Solution:

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A regular hexagon is inscribed in a circle having an area of 158 square. Centimeters. Find the area in circle not covered by the hexagon.

A. 32.34 cm²
B. 27.34 cm²
C. 22.98 cm²
D. 45.63 cm²

Solution:

What is the equation of the radical axis of the circles x²+y² = 1 and x²+y²-6x+6y+11=0?

A. x+2y-2=0
B. x-2y+2=0
C. x+y+2=0
D. x+y+2=0

Solution:

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A mixture compound from 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”. 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”, find the total volume of the two liquids.

A. 523.87 in³
B. 782.12 in³
C. 672.12 in³
D. 603.15 in³

Solution:

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The surface area of a sphere is 3,217 square centimeters. Determine the volume of the sphere in cubic centimeters.

A. 13,982
B. 15,092
C. 17,157
D. 14,764

Solution:

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The corners of a cubical block touch the closed spherical shell that encloses it. The volume of the box is 27,000cc. What volume in cc, inside the shell is not occupied by the block?

A. 46,461
B. 32,987
C. 54,873
D. 28,652

Solution:

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The perimeter of a triangle ABC is 400. If Angle A is 30 degrees and angle B is 58 degrees, find the measure of side AC.

A. 170.23
B. 132.87
C. 144.51
D. 85.26

Solution:

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If sin 3A = cos 6B, find A + 2B in degrees.
A. 30°
B. 60°
C. 45°
D. 15°

Solution:

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The fourth term of an arithmetic progression is -8 and the eighth term is -16. What is the sixth term of the progression?

A. -14
B. -12
C. -10
D. -18

Solution:

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For the sequence 1, 2, 1/2, 1/6, 1/24…, what is the 6^th term?

A. 1/120
B. 1/60
C. 1/48
D. 1/240

Solution:

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“A” can finish a job in 2 days, “B” can finish it in 3 days, and “C” can do it in 6 days. Working together, how many days can they finish the job?

A. 2
B. 3.5
C. 2.5
D. 1

Solution:

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A plane area is bounded by the curve y²=4x and the line y=x.

1. Find the area bounded by the curves.
A. 3.33
B. 3.67
C. 2.67
D. 2.33
2. How far from the x-axis is the centroid of the curve?
A. 2.5
B. 3.3
C. 2
D. 3
3. Find the volume generated if the area is revolved about the x-axis.
A. 42.8
B. 25.8
C. 38.5
D. 33.5

Solution:

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An equipment have a salvage value of P1 million at the end years. The straight-line depreciation charge is P2million.

1. What is the first cost of the machine?
A. P105 million
B. P101 million
C. P103 million
D. P110 million
2. What is its book value after 25 years?
A. P51 million
B. P55 million
C. P49 million
D. P45 million
3. At what year will its total depreciation be P30 million?
A. 14 years
B. 10 years
C. 18 years
D. 15 years

Solution:

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A projectile is fired upward to the right from the top of a 50-m high building with an initial velocity of 200 m/s and an angle of 60° with the horizontal. A wind of 5 m/s is blowing horizontally to the left.

1. Determine the maximum height above the building that the projectile can reach.
A. 1247 m
B. 1087 m
C. 1632 m
D. 1529 m
2. Compute the time for which the projectile reaches its maximum height.
A. 17.7 sec.
B. 18.2 sec.
C. 12.5 sec.
D. 9.6 sec.
3. Determine the y-component of the velocity with which is hits the ground.
A. 196 m/s
B. 201 m/s
C. 185 m/s
D. 176 m/s

Solution:

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The deflection angle from PC of two points A and B on a simple curve are 3°15’ and 8°15’, respectively. The chord distance between A and B is 40 m.

1. Find the length of curve from PC to A.
A. 32m.
B. 36m
C. 26m
D. 28m
2. Find the length of long chord from PC to B.
A. 62.3m
B. 65.9m
C. 71.4m
D. 76.8m
3. What is the radius of the curve?
A. 247.6m
B. 229.5m
C. 258.7m
D. 187.4m

Solution:

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Determine the derivative of y with respect to x of the following equations:

1. x=y³/3
A. 1/y²
B. y²
C. y^-0.5
D. y^0.5
2. y=1/(1-u) where u = 1/(1+x)
A. x²
B. –x^-2
C. x^-2
D. –x²
3. x=y³/3.
A. (3x)^3/2`
B. (3x)^-3/2
C. (3x)^2/3
D. (3x)^-2/3

Solution:

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Evaluate the following limits:

1. Limit of (x²-1)/(x-1) as x approaches 1.
A. 4
B. ¼
C. ½
D. 2
2. Limit of sin (1/x) as x approaches zero.
A. -0.99
B. -0.85
C. -0.75
D. -0.65
3. Limit of (x³-2x²+7)/(2x³+x-3)   as x approaches infinity.
A. 2
B. 4
C. ½
D. ¼

Solution:

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Given the circle x² + y² – 6x + 12y + 9 = 9.

1. What is the radius of the circle?
A. 7.21
B. 6.71
C. 6.28
D. 8.63
2. Where is the center of the circle?
A. (3,-6)
B. (-3,-6)
C. (-3,6)
D. (3,6)
3. Find the shortest distance from the line y = 2x + 10 to the center of the circle.
A. 6.87
B. 10.24
C. 8.49
D. 9.84

Solution:

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