You build an architectural model of a new office complex using a scale factor of 75. Suppose you wanted to fill both the scale model office complex and the actual office complex with marbles. How many times the number of marbles required for the model would be required for the actual building?
Hints:
Actual Length = model length * scale
Actual area = model area * scale²
Actual volume = model volume * scale³
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To determine the number of marbles required for the actual building compared to the scale model, we need to consider the volume relationship between the two.
Since the scale factor is 75, it means that every length measurement on the scale model is 1/75th of the actual length. Therefore, the scale model volume will be (1/75)^3 or 1/421,875 of the actual volume.
To find out how many times the number of marbles required for the actual building is compared to the scale model, we need to calculate the volume ratio between the two.
Let's assume that the scale model requires 'x' number of marbles.
Since the volume ratio between the scale model and the actual building is 1/421,875, the number of marbles required for the actual building will be:
Number of marbles for actual building = (1/421,875) * x
Simplifying the expression:
Number of marbles for actual building = x/421,875
Therefore, the number of marbles required for the actual building is 1/421,875 (approximately 0.00000237) times the number of marbles required for the scale model.
To determine the number of marbles required for the actual building compared to the model, we need to consider the ratio of the scale factor.
The scale factor provided is 75, which means that every dimension (length, width, and height) in the model is 1/75th of the corresponding dimension in the actual office complex.
Since marbles are three-dimensional objects, we need to consider the volume.
The volume ratio between the model and the actual building can be calculated by cubing the scale factor: 75^3 = 421,875.
Therefore, the number of marbles required for the actual building would be 421,875 times the number of marbles needed for the model.