Civil Engineering Online Review

In the triangle ABC, angle C =70°, A= 45°, AB = 40 m. What is the length of the median drawn from the vertex A to side BC?

Solution:

m = 36.3 m.

A sphere having a diameter of 30m. The altitude of the 1st segment is 6 cm. What is the ratio of the area of zone of the second segment to that of the first?

Solution:

Ratio = 4:1

What is the height of a right circular cone having a slant height of √10 x and a base diameter of 2x?

Solution:

By Pythagorean Theorem:

h = 3x

Given is the area in the first quadrant bounded by  x² = 8y, the line x=4 & the x axis. What is the volume generated by revolving this area about the y-axis?

Solution:

By Pappus Proposition:

V= area, circumference

V = 50.265 cu.

The correct distance between two points is 220.45 m. Using a 100 m. tape that is “x” m. too long, the length to be laid on the ground should be 220.406 m. What is the value of “x”?

Solution:

x = 0.02 m.

Solution:

What is the area bounded by the curve y²=x and the line x-4=0?

Solution:

A projectile is fired with a muzzle velocity 300 m/s from a gun aimed upward at an angle of   with the horizontal, from the top of a building 30 m. high a level ground. With what velocity will it hit the ground in m/s?

Solution:

V_B=300.98 m/s

A man paid a 10% down payment of P200,00 for a house and lot and agreed to pay the balance monthly installments for 5 years at  n interest rate of 15% compounded monthly. What was the monthly installment in pesos?

Solution:

R = P42,821.87

How long (years) will it take money to quadruple if it earns 7% compounded semi-annually?

Solution:

x=20.15 years

These sides of a square lot having an area of 2.25 hectares were measured using a 100 m. tape that was 0.04 m. too short. Compute the error in the area in sq.m.

Solution:

A=2.24820036 hectares

Error in area = 2.25-2.24820036

Error in area = 0.00179964 hectares

Error in area = 0.00179964 (10000)

Error in area = 17.9964 sq.m.

Note: 1 hectare = 10000 sq.m.

Cars A and  B Are traveling in the same direction at the same speed at 20 kph along a level road with a Car A 150 m ahead of Car B. Car A decelerates at 2 m/sec². From the instant up to the time B overtakes A, how far has A traveled.

Solution:

S_A = 88.08m.

A pulley that is rotating at 36 rev/s is decelerated at 12 rad/s² until it stops. How many complete revolutions does it make within this period?

Solution:

θ=339 revolutions

A wall “h” meters high is 2m. away from the building. The shortest ladder that can reach the building with one end resting in the ground outside the wall is 6 m. How high is the wall in m?

h=2.245m.

The cross- section notes shown below are for a groun8d excavation for a 10 m. roadway.

What is the volume of excavation in cu.m. between the two station. Use Prismoidal Formula.

Solution:

V=1994.26cu.m.

Note: Dimension of the mid-section is the average of section 1and 2.

The common tangent BC of a reversed curved is 280.5 m. and has a bearing of S 47° 31° E. AB is a tangent of the second curve whose bearing is N. 72°45’ E. CD is a tangent of the second curve whose bearing is N. 38°13’ E. A is at the P.C. while D is at the P.T. The radius of the first curve is 180 m. The P.I. is at the station 12+523.37. Find the stationing of the P.T.

Solution:

Sta. P.T. = 12+878.16

Water is running into hemispherical bowl having a radius of 10 cm. at a constant rate of 3cm³/min. When the water is x cm. deep, the water level is rising at the rate of 0.0149 cm/min. What is the value of x?

Solution:

A 3 degree curve has an angle of intersection of 24°. What is the length of the chord in meters? Uses chord basis.

Solution:

What is the derivative with the respect to x of sec.x of sec.x²?

Solution:

What is the equation of the normal to the curve x²+y²=25 at (4,3)?

Solution:

What is the radius of the circle  x²+y²-6y=0?

Solution:

What is the is the length of the latus rectum of  the curve x²=20y?

Solution:

The number 28, x + 2, 112 from a geometric progression. What is the 10^th term?

Solution:

In how many minutes after 2 o’clock will the hands of the clock extend in the opposite direction for the fist time?

Solution:

What is the sum of the progression 4, 9, 14, 19. . . . up to 20^th term?

Solution: