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Calculating and Measuring

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Swimming Pool. How much water is in an Olympic-size swimming pool that is 50 meters long, 25 meters wide with flat areas 10 meters long at each end, the shallow end being 1 meter deep, the deep end 4 meters? How much chlorine at 1.5 parts per million is required to make the pool safe for swimming?

Crossed Triangles. Two triangles ABC and ADE share a common angle at vertex A. AEB are collinear, with AE = 2 cm and EB = 3 cm. ACD are collinear, with AC = 3. If P is the intersection of BC and DE, and if BP = 4 cm, DP = PE = 2 cm, find the length of DC.

Estimating Speed. A car is driving with its cruise control set on 60 mph, but it takes only 56 seconds to go from one mile marker to the next. How fast is the car really going?

In Between. Find a number between the square root of ten and the square root of 11. Between pi and 3.1456. Between .00009 and .00019. Between 4/11 and 6/17. Between 2^16 and 3^10. Is there any number between .99999... and 1.00000? How do you know?

Roof Angles. A rambler-style house with a 1/5 pitch roof has an attached garage with a 1/4 pitch roof whose orientation is perpendicular to the house. What is the angle of the gutter where the two roofs join?

Carpet Cleaning. A carpet cleaner needs to submit a bid on cleaning the doughnut-shaped carpet in a revolving restaurant. He knows only that the room is 24 feet wide and that the distance around the inner hole is 144 ft. If he normally charges $50 plus $3.00 per square yard, what bid should he submit?

Losing Weight. A store has 100 lbs of cucumbers that are 99% water. After they sit in storage for a while some of the water evaporates, so that then they are sold they are only 98% water. What do they weigh when they are sold?

Seeing the Horizon. How far can you see from an airplane flying at 36,000 feet?

Road Grades. What is the slope of a road that rises at a 6% grade? How long does the road have to be to enable a car to climb 100 feet? What if the maximum allowable grade is 4%?

Roofing. A 30' x 60' rambler has a 3/12 pitch hip roof that hangs over 4' on all sides. Find the area of the roof to determine how many shingles to purchase.

Pouring Concrete. You have decided to build a 12' by 20' deck, with the long side attached to your house. The outer edge will be supported by four posts resting on cylindrical concrete piers whose footings must be 48 inches below grade level to prevent frost heaves. Standard design specifications for decks require that you allow 50 lbs per square foot--10 for the deck, and 40 for people and furniture. If the soil has a bearing capacity of 1500 lbs per square foot, how much concrete do you need for the supporting piers?

Chimney Skirts. A round chimney 8" in diameter protrudes from a roof that has a pitch of 1:2. Draw a pattern for an aluminum skirt that can be cut out of sheet metal and bent into a cone to seal the chimney against rain.

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Last Update: 12/29/98