The volume of metal in a scale model of an mobile phone tower is 54 cm^3. The scale was 1:50. It required 5 ml of paint to give the model one coat.
Find the volume of mental in cubic metres would be required to build the tower.
the scale of volume is the cube of the linear scale, since each dimension is multiplied by the scale.
Then convert that using 1m = 100 cm
The result says that
v = 54 cm^3 * (50/1)^3 * (1m/100cm)^3 = 54*(1/2)^3 = 54/8 = 27/4 m^3
To find the volume of metal in cubic meters required to build the tower, we need to first calculate the volume of the scale model in cubic meters.
Given that the volume of the scale model is 54 cm^3 and the scale is 1:50, we can find the volume of the scale model in cubic meters using the following steps:
1. Convert the volume from cubic centimeters (cm^3) to cubic meters (m^3).
1 cm^3 = 0.000001 m^3 (since 1 meter = 100 cm)
So, the volume of the scale model in cubic meters = 54 cm^3 x 0.000001 m^3/cm^3 = 0.000054 m^3
Next, we need to determine the volume ratio between the scale model and the actual tower. Since the scale is 1:50, it means that the dimensions of the scale model are 1/50 times smaller than the actual tower.
To calculate the volume ratio, we need to cube the scale ratio (1/50) since volume is a three-dimensional measurement.
Volume ratio = (1/50)^3 = 1/125,000
Now, we can find the volume of metal in the actual tower by multiplying the volume of the scale model by the volume ratio:
Volume of metal in the tower = 0.000054 m^3 x (1/125,000) = 0.000000432 m^3
Therefore, the volume of metal required to build the tower is 0.000000432 cubic meters.