A scale model of an office building is 3' x 2' x 5' (length, width, height). If the actual building has a length of 45 feet, what is the volume of the actual building?
81,000 cubic feet
102,150 cubic feet
101,250 cubic feet
30,000 cubic feet

Question

A scale model of an office building is 3' x 2' x 5' (length, width, height). If the actual building has a length of 45 feet, what is the volume of the actual building?
81,000 cubic feet
102,150 cubic feet
101,250 cubic feet
30,000 cubic feet

jadedry · Answer

@ericmabry


If 3' is the length of the model

and 45' is the length of the building

it means that the building is 45/3 = 15 times longer than the scale. 

Has an area  (15^2) times larger than the scale.

And a volume  (15^3) times larger than the scale. 

You have two options:

Convert all scale lengths to real lengths and multiply:

$$(3*15) * (2*15) * (5*15) = 101 250 $$

Or find the volume of the scale model:
$$3*2*5 = 30$$

$$30 * (15^3)$$

=$$101 250$$

either way you get the same answer.