# 2016 May

## Partially Filled Cylindrical Tank Rotated at 90 rpm

**Situation**

An open cylindrical vessel 1.3 m in diameter and 2.1 m high is 2/3 full of water. If rotated about the vertical axis at a constant angular speed of 90 rpm,

1. Determine how high is the paraboloid formed of the water surface.

A. 1.26 m | C. 2.46 m |

B. 1.91 m | D. 1.35 m |

2. Determine the amount of water that will be spilled out.

A. 140 L | C. 341 L |

B. 152 L | D. 146 L |

3. What should have been the least height of the vessel so that no water is spilled out?

A. 2.87 m | C. 3.15 m |

B. 2.55 m | D. 2.36 m |

## Slope of a Curve with Given Parametric Equations

**Problem**

A point moves in the plane according to equations *x* = *t*^{2} + 2*t* and *y* = 2*t*^{3} - 6*t*. Find *dy*/*dx* when *t* = 0, 2, 5.

A. -3, -3, -12 | C. 3, 3, 12 |

B. 3, -3, 12 | D. -3, 3, 12 |

## Distance From a Point to a Plane

**Problem**

Find the distance from the point *A*(1, 5, -3) to the plane 4*x* + *y* + 8*z* + 33 = 0.

A. 1/2 | C. 2/3 |

B. 2 | D. 1.5 |

## Area Bounded by Intersecting Chords in a Circle

**Problem**

Chords *AB* and *CD* intersect each other at *E* inside the circle. *AE* = 8 cm, *CE* = 12 cm, and *DE* = 20 cm. If *AB* is the diameter of the circle, compute the area of *AEC*.

A. 61.04 cm^{2} |
C. 39.84 cm^{2} |

B. 52.05 cm^{2} |
D. 48.62 cm^{2} |

## Absolute Pressure at 200 mm Below the Surface of Liquid Mercury

**Problem**

Determine the absolute pressure in a vessel of mercury at a point 200 mm below its surface.

A. 126 kPa | C. 128 kPa |

B. 130 kPa | D. 132 kPa |

## Truss With Tension-Only Diagonals

**Situation**

Diagonals *BG*, *CF*, *CH*, and *DG* of the truss shown can resist tension only.

If *W* = 3 kN and *P* = 0, find the following:

1. the force in member *CF*.

A. 4.76 kN | C. 4.67 kN |

B. 4.32 kN | D. 4.23 kN |

2. the force in member *BF*.

A. 3.2 kN | C. 3.4 kN |

B. 3.3 kN | D. 3.5 kN |

3. the force in member *DH*.

A. 2.8 kN | A. 2.5 kN |

B. 2.8 kN | D. 2.7 kN |

## Fundamental Frequency of Fourier Equation in Cosine Form

**Problem**

Given the Fourier equation:

*f*(

*t*) = 5 cos (20π

*t*) + 2 cos (40π

*t*) + cos (80π

*t*)

What is the fundamental frequency?

A. 10 | C. 40 |

B. 20 | D. 30 |

## Truss With Flexible Cable Diagonals

**Situation**

Flexible cables *BE* and *CD* are used to brace the truss shown below.

1. Determine the load *W* to cause a compression force of 8.9 kN to member *BD*.

A. 7.80 kN | C. 26.70 kN |

B. 35.64 kN | D. 13.35 kN |

2. Which cable is in tension and what is the tensile reaction?

A. BE = 12.58 kN |
C. BE = 6.29 kN |

B. CD = 6.29 kN |
D. CD = 12.58 kN |

3. If *W* = 20 kN, what will be the tensile reaction of member *CE*?

A. 6.67 kN | C. 0 |

B. 13.33 kN | D. 10 kN |

## Find the Integral of dx / sqrt(1 + sqrt(x))

**Problem**

Evaluate $\displaystyle \int_0^9 \dfrac{1}{\sqrt{1 + \sqrt{x}}}$

A. 4.667 | C. 5.333 |

B. 3.227 | D. 6.333 |