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?
I got 31.9cm (just need help on part b!)
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?
if the model has diameter 31.9 cm,
its area is π*31.9^2 = 3196.92 cm^2
So, divide that by 2 and then by 10 to get the number of jars
but the answer our teacher gave us is 240 jars im so confusde
To get the answer to part b, we need to calculate the surface area of each half of the model and then divide it by the coverage area of one jar of paint.
Step 1: Calculate the surface area of a sphere
The formula for the surface area of a sphere is: 4πr^2, where r is the radius of the sphere.
Since we are dealing with the diameter, which is 31.9 cm, we need to divide it by 2 to get the radius.
Radius (r) = diameter / 2
r = 31.9 cm / 2
r = 15.95 cm
Step 2: Calculate the surface area of the model
Surface area = 4πr^2
Surface area = 4 * 3.14159 * (15.95 cm)^2
Now, calculate the surface area of the model and divide it by 2 since we are splitting it in half.
Surface area of each half = (4 * 3.14159 * (15.95 cm)^2) / 2
Step 3: Calculate the number of jars of paint needed
Now, we divide the surface area of each half by the coverage area of one jar of paint, which is 10 cm^2.
Number of jars needed = (Surface area of each half) / 10 cm^2
Plug in the values and calculate:
Number of jars needed = ((4 * 3.14159 * (15.95 cm)^2) / 2) / 10 cm^2
Simplify the equation and calculate the answer to part b.