Problems using proportionality. Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer?

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Presentation transcript:

problems using proportionality

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer?

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer? At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling.

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer? At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling. t  d

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer? At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling. t  d When running a mile, one runs a distance 1.6 times less. The time running is proportional. It is 1.6 times less.

Robert runs a mile in 4.0 minutes. At the same speed, how fast does he run a kilometer? At constant speed of travel, d, the distance travelled is proportional to t, the amount of time spent travelling. t  d When running a mile, one runs a distance 1.6 times less. The time running is proportional. It is 1.6 times less. 4 ____ =

A bronze copy is made out of exactly the same material and in exactly the same proportions as the the NYC Statue of Liberty but reduces its volume from the NYC volume of 4000 m 3 to 2 m 3. The original mass is 3 x 10 7 kg. What is the mass of the new copy? Jardin du Luxembourg

each MK82 bomb has 89 kg lbs TNT and delivers 4.1 x 10 5 kJ Vietnam 1965 To one significant figure, how much energy does the new bunker buster deliver?

proportionality relations II

What is formula relating volume of a cube to the length of the side of the cube? We call the length of a side of cube 2r. What is formula relating volume of a sphere to the length of the radius of sphere? We call the radius of a sphere r. 2r r

What is the proportionality relation between V and r? To one significant figure what is proportionality constant? 2r r What is the proportionality relation between V and r? To one significant figure what is proportionality constant? 2r

V  r 3 proportionality constant = 8 2r r V  r 3 proportionality constant ≈ 4 Volume of sphere and cube have exactly the same proportionality relation. Only proportionality constant is different.

V great pyramid = 1⅔ r 3 Egyptian great pyramids often have similar proportions. The width is approximately 8/5 times the height. What is the proportionality relation between volume and r? What is the proportionality constant?

V  r 3 2r r If shape is fixed then no matter what the shape, volume always proportional to the side cibed If shape is fixed then, no matter what the shape, volume always proportional to a length cubed.