Units of Measurement

This topic deals with standard quantities used to express physical amounts, such as length (meters, feet), mass (kilograms, pounds), time (seconds, hours), and volume (liters, gallons). Questions involve converting between different units and solving word problems that require consistent use of units.

  • Question

    Samuel wants to tile a room measuring `3` by `4` meters using square tiles with a side length of `25` centimeters. How many tiles does Samuel need?

  • Question

    A cube with a side length of one meter is cut into cubes with a side length of one centimeter. If all the resulting cubes are placed in a row, what will be the length of the row?

  • Question

    How long will it take a train traveling at a speed of `60` km/h and with a length of `50` meters to pass through a tunnel with a length of `50` meters?

  • Question

    A cube with a side of one meter is cut into cubes with a side of one centimeter. If we put all the resulting cubes in a row, what will be the length of the row (in kilometers)?

  • A NEW MONEY PUZZLE

    The largest sum of money that can be written in pounds, shillings, pence, and farthings, using each of the nine digits once and only once, is 拢`98,765, 4`s. `3`陆d. Now, try to discover the smallest sum of money that can be written down under precisely the same conditions. There must be some value given for each denomination鈥攑ounds, shillings, pence, and farthings鈥攁nd the nought may not be used. It requires just a little judgment and thought. Sources:

  • THE GROCER AND DRAPER

    A country "grocer and draper" had two rival assistants, who prided themselves on their rapidity in serving customers. The young man on the grocery side could weigh up two one-pound parcels of sugar per minute, while the drapery assistant could cut three one-yard lengths of cloth in the same time. Their employer, one slack day, set them a race, giving the grocer a barrel of sugar and telling him to weigh up forty-eight one-pound parcels of sugar While the draper divided a roll of forty-eight yards of cloth into yard pieces. The two men were interrupted together by customers for nine minutes, but the draper was disturbed seventeen times as long as the grocer. What was the result of the race? Sources:

  • THE CLUB CLOCK

    One of the big clocks in the Cogitators' Club was found the other night to have stopped just when, as will be seen in the illustration, the second hand was exactly midway between the other two hands. One of the members proposed to some of his friends that they should tell him the exact time when (if the clock had not stopped) the second hand would next again have been midway between the minute hand and the hour hand. Can you find the correct time that it would happen? Sources:

  • A FENCE PROBLEM

    The practical usefulness of puzzles is a point that we are liable to overlook. Yet, as a matter of fact, I have from time to time received quite a large number of letters from individuals who have found that the mastering of some little principle upon which a puzzle was built has proved of considerable value to them in a most unexpected way. Indeed, it may be accepted as a good maxim that a puzzle is of little real value unless, as well as being amusing and perplexing, it conceals some instructive and possibly useful feature. It is, however, very curious how these little bits of acquired knowledge dovetail into the occasional requirements of everyday life, and equally curious to what strange and mysterious uses some of our readers seem to apply them. What, for example, can be the object of Mr. Wm. Oxley, who writes to me all the way from Iowa, in wishing to ascertain the dimensions of a field that he proposes to enclose, containing just as many acres as there shall be rails in the fence? The man wishes to fence in a perfectly square field which is to contain just as many acres as there are rails in the required fence. Each hurdle, or portion of fence, is seven rails high, and two lengths would extend one pole (`16`陆 ft.): that is to say, there are fourteen rails to the pole, lineal measure. Now, what must be the size of the field? Sources:

  • A QUESTION OF DEFINITION

    "My property is exactly a mile square," said one landowner to another.

    "Curiously enough, mine is a square mile," was the reply.

    "Then there is no difference?"

    Is this last statement correct?

    Sources:

  • A KITE-FLYING PUZZLE

    While accompanying my friend Professor Highflite during a scientific kite-flying competition on the South Downs of Sussex I was led into a little calculation that ought to interest my readers. The Professor was paying out the wire to which his kite was attached from a winch on which it had been rolled into a perfectly spherical form. This ball of wire was just two feet in diameter, and the wire had a diameter of one-hundredth of an inch. What was the length of the wire?

    Now, a simple little question like this that everybody can perfectly understand will puzzle many people to answer in any way. Let us see whether, without going into any profound mathematical calculations, we can get the answer roughly—say, within a mile of what is correct! We will assume that when the wire is all wound up the ball is perfectly solid throughout, and that no allowance has to be made for the axle that passes through it. With that simplification, I wonder how many readers can state within even a mile of the correct answer the length of that wire.

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