Marco is making a scale model of a building. The building has a round deck at the bottom with a diameter of 120 meters. What should the diameter of the deck in the scale model be if Marco wants the circumference to be 1/40 actual size?

if the circumference is 1/40 as big, then so is the diameter.

To find the diameter of the deck in the scale model, we can use the scale factor. The scale factor is the ratio between the dimensions of the actual object and the scale model. In this case, the scale factor is 1/40 because Marco wants the circumference of the deck in the scale model to be 1/40 of the actual size.

Let's start by finding the circumference of the actual deck. The formula for the circumference of a circle is C = πd, where C is the circumference and d is the diameter.

C_actual = π * d_actual

Since the diameter of the actual deck is given as 120 meters, we can substitute this value into the formula:

C_actual = π * 120

Next, we need to find the circumference in the scale model, which is equal to 1/40 of the actual size:

C_model = 1/40 * C_actual
= 1/40 * (π * 120)

Now, we can find the diameter of the deck in the scale model using the formula for circumference:

C_model = π * d_model

Substituting the value of C_model, the formula becomes:

1/40 * (π * 120) = π * d_model

To find d_model, isolate it on one side of the equation:

d_model = (1/40 * (π * 120)) / π

Simplifying the equation:

d_model = (1/40) * 120
= 3

Therefore, the diameter of the deck in the scale model should be 3 meters.