March 2014

032 Review Problem - How many cups of coffee a coffee pot can hold?

Problem 32
A coffee pot is 5 in. deep, 4-1/2 in. in diameter at the top, and 5-3/4 in. in diameter at the bottom. How many cups of coffee will it hold if 6 cups equal 1 quart? Answer to the nearest whole number.
 

033 Review Problem - Finding which one is the better bargain

Problem 33
Disregarding quality, and considering oranges as spheres, determine which is the better bargain, oranges 2-3/4 in. in diameter at 15 cents per dozen, or oranges averaging 3-1/2 in. in diameter at 30 cents per dozen.
 

034 Review Problem - Sphere dropped into a cone

034-cone-sphere.gifThe inside of a vase is an inverted cone 2.983 in. across the top and 5.016 in. deep. If a heavy sphere 2.498 in. in diameter is dropped into it when the vase is full of water, how much water will overflow?
 

035 Review Problem - Amount of concrete in a caisson

Problem 35
In the foundation work of the Woolworth Building, a 55-story building in New York City, it was necessary, in order to reach the bedrock, to penetrate the sand and quicksand to a depth, in some instances, of 131 ft. If the largest circular caisson, 19 ft. in diameter, was 130 ft. deep and was filled with concrete to within 30 ft, of the surface, how many cubic yards of concrete were required?
 

036 Review Problem - Circular hole bored through a sphere

Problem 36
A hole 6 in. in diameter was bored through a sphere 10 in. in diameter. Find the volume of the part cut out.
 

036-sphere-with-hole.gif

 

037 Review Problem - Amount of material the factory chimney contain

Problem 37
A factory chimney is in the form of frustum of regular square pyramid. The chimney is 125 ft. high the edges of its bases are 12 ft. and 8 ft., respectively. The cross-section of the flue is 6 ft. square. How many cubic feet of material does the chimney contain?
 

037-chimney.jpg

 

038 Review Problem - Circular log with non-uniform cross-section

Problem 38
A log 18 ft. long is 2 ft. in diameter at the top end and 3 ft. in diameter at the butt end.
 

038-circular-log.gif

 

  1. How many cubic feet of wood does the log contain?
  2. How many cubic feet are there in the largest piece of timber of square cross section that can be cut from the log?
  3. How many cubic feet are in the largest piece of square timber of the same size throughout its whole length?
  4. How many board feet does the piece of timber in (c), a board foot being equivalent to a board 1 ft. square and 1 in. thick?

Hint: In (b) the larger end is the square ABCD. What is the smaller end? In (c) one end is the square EFGH. What is the other end?

039 Review Problem - Bushels of wheat the grain elevator can hold

Problem 39
A grain elevator in the form of a frustum of a right circular cone is 24 ft. high, and the radii of its bases are 10 ft. and 5 ft., respectively; how many bushels of wheat will it hold if 1-1/4 cu. ft. equals 1 bu.?
 

040 Review Problem - Volume comparisons of two water crystals

Problem 40
When a liquid freezes, it changes into a mass of solid bodies, each of which has a definite geometric form and is known as a crystal. Crystals are always bounded by plane surfaces, which are arranged in an orderly fashion with reference to imaginary lines drawn through the crystal and called its area. Every crystal has therefore a definite geometric form. Compare the volumes of crystals, one in the shape of a hexagonal right prism 'a' units on a side and '2a' units in altitude, and the other in the shape of two oppositely directed hexagonal regular pyramids, each 'a' units high with a common base 'a' units on a side.
 

040-water-crystal-3d.jpg

 

041 Review Problem - Weight capacity of industrial soap kettle

Problem 41
Soap kettles used in the commercial manufacture of soap are as a rule large cylindrical vats, 50,000 lb. or more of soap being made in a single beating. Find the capacity of such a kettle having an inside diameter of 18 ft and an altitude of 30 ft. if soap weighs 70 lb. per cu. ft.
 

042 Review Problem - Water is poured by tilting the glass

Problem 42
From a cylindrical glass 6 in. high and 3 in. in diameter, water is poured by tilting the glass until the highest point of the bottom of the glass lies in the plane of the water surface. How much water remains?
 

042-tilted-glass-3d.jpg

 

12 - Circular sector inscribed in a square

Problem 12
A circular sector of radius 10 cm is inscribed in a square of sides 10 cm such that the center of the circle is at the midpoint of one side of the square. Find the area of the sector in cm2.
 

012-sector-inscribed-square_big.gif

 

Problem 815 | Continuous Beam by Three-Moment Equation

Problem 815
Find the moment at R2 and R3 of the continuous beam shown in Fig. P-815.
 

815-continuous-beam-triangular-concentrated-loads.gif

 

Problem 816 | Continuous Beam by Three-Moment Equation

Problem 816
Determine the lengths of the overhangs in Fig. P-816 so that the moments over the supports will be equal
 

816-equal-moments-over-supports.gif

 

Problem 817 | Continuous Beam by Three-Moment Equation

Problem 817
Find the moment under the support R2 of the continuous beam shown in Fig. P-817.
 

817-continuous-beam-with-moment-and-triangular-loads.gif

 

Problem 818 | Continuous Beam by Three-Moment Equation

Problem 818
In Problem 817, determine the changed value of the applied couple that will cause M2 to become zero.
 

818-continuous-beam.gif

 

Problem 819 | Continuous Beam by Three-Moment Equation

Problem 819
Find the moment under the supports R2 and R3 for the beam shown in Fig. P-819.
 

819-length-of-spans-continuous-beams.gif

 

Problem 820 | Continuous Beam by Three-Moment Equation

Problem 820
Solve Prob. 819 if the concentrated load is replaced by a uniformly distributed load of intensity wo over the first span.
 

820-continuous-beam-uniform-load.gif