The scale for an earth model is 1:40000000. The diameter of the earth is 12,756.32km. a)What is the diameter of the model in cm?
b) If the model is cut in half, how many jars of paint would be needed to paint each half if 1 jar covered 10cm^2?
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2) 15
um.. a) is supposed to be 31.9cm and b) is 240jars but i don't know how to get there.
To find the diameter of the model in cm, we need to convert the diameter of the Earth in km to cm using the given scale.
a) Diameter of the model in cm:
1 km = 100,000 cm, so we can convert the diameter of the Earth from km to cm by multiplying by 100,000.
Diameter of the Earth in cm = 12,756.32 km * 100,000 cm/km
Diameter of the Earth in cm = 1,275,632,000 cm
Now, to find the diameter of the model, we need to apply the scale. The scale 1:40000000 means that 1 cm on the model represents 40,000,000 cm in reality.
Diameter of the model in cm = Diameter of the Earth in cm / Scale
Diameter of the model in cm = 1,275,632,000 cm / 40,000,000
Diameter of the model in cm = 31.89 cm
b) If the model is cut in half, we need to find the surface area of each half to determine the amount of paint needed.
Surface area of a hemisphere = 2 * π * r^2
Since the model is cut in half, the radius (r) would be half the diameter of the model.
Radius (r) = 31.89 cm / 2
Radius (r) = 15.95 cm
Surface area of each half = 2 * π * (15.95 cm)^2
Surface area of each half = 2 * 3.14 * (15.95 cm)^2
Surface area of each half ≈ 2013.26 cm^2
If 1 jar of paint covers 10 cm^2, the number of jars needed to paint each half would be:
Number of jars needed = Surface area of each half / 10 cm^2
Number of jars needed ≈ 2013.26 cm^2 / 10 cm^2
Number of jars needed ≈ 201.33 jars (rounded up to the nearest whole number)
Therefore, approximately 202 jars of paint would be needed to paint each half of the model.