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1234Using formulas

Exercises

Exercise 1

The volume of a cylindrical tin can is given by: V = π r 2 h .
Here V is the volume, r the radius in centimeters and h the height in centimeters.

a

In what unit should V be expressed?

b

What is the volume of a tin can with a diameter of 80 millimeters and a height of 16 centimeters?

c

What formula expresses the relationship between V and r for cans with a height of 16 centimeters?

d

Draw a graph for the formula you found in c.

e

For other cans the volume is known: V = 1 L. What relationship is there between r and h ? Draw a corresponding graph.

Exercise 2

Which of these formulas describes a relation between two variables? Draw a graph for the ones that do.

a

( 2 + x ) y = 2 y + x y

b

volume(cube) = r 3

c

s = 400 - 5 t 2

d

a 2 + b 2 = c 2

Exercise 3

When you use electricity you pay a fixed charge per year and a variable cost per kWh (kiloWatthour). The total yearly cost depends on the number of kWh's used. It is possible to convert the total cost to cost per kWh. This gives the formula:
K = 0,12 + 32 a
Here a is the number of kWh used and K the cost per kWh (in euro).

a

What is the fixed cost per year?

b

Draw a graph of K as a function of a . Why should K be on the vertical axis?

c

For what value of a is the cost per kWh 16 eurocent?

Exercise 4

An electrical resistor is connected to a power source of 200 Volts. An ammeter can be used to measure the electrical current. Ohm's law is valid in this situation: U = I R where U is the power voltage V (volt), I the electrical current in A (ampère) and R the resistance in Ω (ohm).

a

For a power voltage of 200 volts Ohm's law gives the relation between I and R . What is this formula? And what units belong to this formula?

b

Draw the corresponding graph.

c

What current is measured when R = 15 Ω?

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