# calculating derived quantities

## units of derived quantities

A given derived quantity, such as area, is always expressed in the same type of units. For example, area is always expressed in squared units, such as cm2 or m2 . If you calculate area and your answer isnt in squared units, then you have made an error. Q: What units are used to express volume? A: Volume is expressed in cubed units, such as cm3 or m3 . Q: A certain derived quantity is expressed in the units kg/m3 . Which derived quantity is it? A: The derived quantity is density, which is mass (kg) divided by volume (m3 ).

## calculating density

Density is a quantity that expresses how much matter is packed into a given space. The amount of matter is its mass, and the space it takes up is its volume. To calculate the density of an object, then, you would use this formula: Density = mass volume Q: The volume of the blue rectangular solid above is 150 cm3 . If it has a mass of 300 g, what is its density? A: The density of the rectangular solid is: Density = 300 g = 2 g/cm3 150 cm3 Q: Suppose you have two boxes that are the same size but one box is full of feathers and the other box is full of books. Which box has greater density? A: Both boxes have the same volume because they are the same size. However, the books have greater mass than the feathers. Therefore, the box of books has greater density.

## calculating volume

The volume of a solid object is how much space it takes up. Its easy to calculate the volume of a solid if it has a simple, regular shape, such as the rectangular solid pictured in the sketch below. To find the volume of a rectangular solid, use this formula: Volume (rectangular solid) = length width height (l w h) Q: What is the volume of the blue rectangular solid? A: Substitute the values for the rectangular solids length, width, and height into the formula for volume: Volume = 10 cm 3 cm 5 cm = 150 cm3

## calculating area

The area of a surface is how much space it covers. Its easy to calculate the area of a surface if it has a regular shape, such as the blue rectangle in the sketch below. You simply substitute measurements of the surface into the correct formula. To find the area of a rectangular surface, use this formula: Area (rectangular surface) = length width (l w) Q: What is the area of the blue rectangle? A: Substitute the values for the rectangles length and width into the formula for area: Area = 9 cm 5 cm = 45 cm2 Q: Can you use this formula to find the area of a square surface? A: Yes, you can. A square has four sides that are all the same length, so you would substitute the same value for both length and width in the formula for the area of a rectangle.

## what are derived quantities

Derived quantities are quantities that are calculated from two or more measurements. Derived quantities cannot be measured directly. They can only be computed. Many derived quantities are calculated in physical science. Three examples are area, volume, and density.

## instructional diagrams

No diagram descriptions associated with this lesson

## questions

derived quantities cannot be measured directly.

``````-->  a. true

b. false
``````

examples of derived quantities include:

``````a) area.

b) volume.

c) density.

-->  d) all of the above
``````

which units could be used to measure volume?

``````a) ml

b) m2

c) mm3

-->  d) two of the above
``````

the units m/s represent

``````a) area.

-->  b) speed.

c) density.

d) pressure.
``````

## diagram questions

No diagram questions associated with this lesson