Question

Going to bed soon, but if I could get help with this before that would be great! :)

The scale model of a Lamborghini sports car is 1:200. If it requires 12 litres of paint for the real car, how much paint is needed for the scale model in mL? (1 litre = 1000mL)

These Scale questions really confuse me! :/

Answer 1

Let's say we had a cube with each side length of 1 unit



what is the surface area of this cube?

Answer 2

1 Cubic unit

Answer 3

that's the volume

Answer 4

I want to know the total area of each face

Answer 5

oh sorry.. the area is 1*6? so SA= 6

Answer 6

good

Answer 7

now let's say I multiplied every dimension by 200

that's what it means when it says the scale is 1:200

the initial is 1 and the larger is 200 times that

Answer 8

so let's say we now have this much larger cube with side lengths of 200

Answer 9

what is the surface area of that new (much larger) cube?

Answer 10

200*200 = 40000
40000*6 =240000
SA= 240000 ?

Answer 11

correct

Answer 12

so we've gone from 6 to 240,000

Answer 13

notice how 240,000/6 = 40,000

and how (200)^2 = 40,000

this is no coincidence

Answer 14

it turns out that if you know the smaller surface area, you multiply by (200)^2 = 40,000 to get the larger surface area

or you can go in reverse: if you know the larger surface area, you can divide by 200^2 = 40,000 to get the smaller surface area

Answer 15

This works all based on ratios. In general, if you have a cube with side length of 1 and then it jumps to side length of k, then...


SA of cube with side length 1: SA = 6*1^2 = 6

SA of cube with side length k: SA = 6*k^2 = 6k^2

Ratio of larger to smaller: (6k^2)/6 = k^2 ---> ratio is k^2 : 1

Ratio of smaller to larger: 6/(6k^2) = 1/(k^2) ---> ratio is 1 : k^2

Answer 16

Okay! So is 40,000 the SA of the model? And 240 000 the SA of the real car?

Answer 17

not quite, the 40,000 is based off the example of the cube I drew

Answer 18

oh nvm

Answer 19

but 40,000 isn't the answer

it helps us get there though

Answer 20

so we know the entire real car takes 12 liters of paint

12 L = 12*1000 mL

12 L = 12000 mL

So it takes 12,000 mL of paint