A log cabin in the shape of a rectangular prism is modeled using a scale of 1 cm : 0.6 m. If the dimensions
of the model are 34 × 20 × 6 centimeters, what is the volume of the actual log cabin?
To find the volume of the actual log cabin, we need to first convert the dimensions of the model from centimeters to meters, using the scale given.
The scale is 1 cm : 0.6 m, so we can set up the following proportion:
1 cm / 0.6 m = 34 cm / x
To solve for x, we can cross multiply and then divide:
1 * x = 0.6 * 34
x = 0.6 * 34 / 1
x = 20.4 m
Similarly, we can convert the other dimensions of the model to meters:
1 cm / 0.6 m = 20 cm / y
1 * y = 0.6 * 20
y = 0.6 * 20 / 1
y = 12 m
1 cm / 0.6 m = 6 cm / z
1 * z = 0.6 * 6
z = 0.6 * 6 / 1
z = 3.6 m
Now, using the dimensions of the actual log cabin (34 m × 20 m × 6 m), we can calculate its volume:
Volume = Length × Width × Height
Volume = 34 m × 12 m × 3.6 m
Volume ≈ 1468.8 cubic meters
Therefore, the volume of the actual log cabin is approximately 1468.8 cubic meters.
Scale = 1cm:0.6m = 1cm:60cm
V = (60/1)*(34 x 20 * 6)
V = 2040 x 1200 x 360 cm.