The volume of air in a model car is #40cm^3# . A scale of 1:50 was used to create the model. What is the volume of air in the actual car?

I got the answer #2000cm^3# .
Is that right?

4 Answers
Jul 23, 2018

#V_("air in the actual car") = 5,000,000 cm^3#

Explanation:

Given: #V_("air in the model") = 40 cm^3#. Scale of #1:50# model to actual.

The scale #1:50# is a linear scale. This means for each centimeter in length, width and height of the model, there is #50# centimeters in length, width and height in the actual model.

The volume scale is then #50^3 #

#V_("air in the actual car") = 40 cm^3 xx 50^3 = 5,000,000 cm^3#

#"5,000,000"cm^3=5m^3#

Explanation:

Let's think about the calculation this way:

Let's say we have a line segment and it's length 1. We then want to scale that line using the 1:50 ratio. Our scaled line segment will be length 50. Very straightforward calculation.

Let's now look at a square. It's got length of 1 and width of 1 and an area of 1 unit squared. Let's now apply the scale. What happens? The length is now 50 and the width is also 50. The area of the square is #50xx50=2500# units squared.

The same thing happens when we move to three dimensions: our cube with length 1, width 1, height 1, and volume 1 unit cubed, when scaled, now has width 50, length 50, height 50 and volume #50xx50xx50="125,000"# units cubed.

Let's now move to our question. We have a car that has a volume of 40 cm cubed. What factor do we use for scaling to the actual size of the car? #"125,000"#. So we end up with the original car having:

#40xx"125,000"="5,000,000"cm^3=5m^3# of air.

Jul 25, 2018

See below

Explanation:

If #1/50# was a linear ratio, meaning that it was applied to each of the three dimensions of the car and not just the volume then:

#(40 cm^3)/x= (1)^3/(50)^3#

#x= 40cm^3*50^3=5000000" cm"^3"#

To convert to meters cubed if you wanted:

#5000000 "cm"^3xx(1 m)^3/(100 cm)^3= 5 m^3#

Jul 26, 2018

#5m^3# is the volume of the real car.

Explanation:

It is important to realise that the model and the real car are similar figures.

They have exactly the same shape, but different sizes.
The scale is #1 : 50# which means that all lengths on the real car are #50# times bigger than on the model.

In similar figures, their volumes are in the same ratio as the cube of the lengths.

#1^3/50^3 = (40cm^3)/x" "(larr "model")/(larr "real car")#

#x = 50^3 xx 40 cm^3#

#x = 5,000,000 cm^3#

This is not a practical unit, convert to #m^3#

#(5,000,000)/(1000xx1000)#

#= 5m^3#