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Mathematics

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My name is Ann [436]3 years ago

8 0

We have to calculate the volume of the right rectangular prism.
lenght=4 1/2 in=(4+1/2) in=9/2 in
width=5 in
height=3 3/4 in=(3+3/4) in=15/4 in

Volume (right rectangular prism = lenght x width x height.
volume=9/2 in * 5 in * 15/4 in=675/8 in³

we calculate the volume of this little cube.
volume=side³
volume=(1/4 in )³=1/64 in³

Now, we calculate the number of small cubes are needed to fit the right rectangular pris by the rule of three.

1 small cube----------------1/64 in³
x---------------------------------675/8 in³

x=(1 small cube * 675/8 in³) / 1/64 in³=5400 small cubes.

Answer: we need 5400 small cubes to fit the right rectangular prism.

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If a scale distance of 3.5 inches on a map represent an actual distance of 175 km what actual distance does a scale distance of

gavmur [86]

Considering the definition of map and scale, an actual distance of 269.59 km represent a scale distance of 5.7 inches .

<h3>Definition of map and scale</h3>

A map is a representation of a place, at a size smaller than the real size.

The scale of a cartographic representation is the relationship of similarity between the real dimensions of the geographical space represented and those of its image on the map. That is, the scale is defined as the proportionality relationship that exists between a distance measured on the ground and its corresponding measurement on the map.

One way to represent the scale is by a fraction, which indicates the proportion between the distance on a map and its corresponding distance in reality:

$Scale=\frac{distance on the map}{distance in reality}$

<h3>Actual distance in this case</h3>

In this case, you know that a scale distance of 3.5 inches on a map represent an actual distance of 175 km.

To know the real distance that represents a scale distance of 5.7 inches, as the scale ratio is the same as in the previous case, it is expressed:

$\frac{3.7 inches}{175 km}=\frac{5.7 inches}{distance in reality}$