The surface area A of a sphere of radius R is given by the equation A = 4pi*R2, where pi equals 3.1416 (to 5 digits). Calculate the area of a sphere which has a radius of 2 m.
If 2600 grains of sand are uniformly spread out on the surface of the sphere, how many grains of sand are there on each square meter? HINT: We need to divide the number of grains of sand by the number of square meters of the sphere's surface.
To calculate the surface area of a sphere with a radius of 2 meters, we can use the given equation: A = 4πR^2.
First, substitute the given radius value, R = 2, into the equation:
A = 4π(2)^2
= 4π(4)
= 16π
Now, we are asked to find the number of grains of sand on each square meter of the sphere's surface. To do this, we need to divide the total number of grains of sand by the total surface area of the sphere.
Given that there are 2600 grains of sand uniformly spread out on the surface of the sphere, we can divide this value by the surface area we calculated earlier, 16π.
Number of grains of sand per square meter = 2600 / (16π)
To simplify the calculation, let's approximate pi to 3.1416.
Number of grains of sand per square meter ≈ 2600 / (16 * 3.1416)
Now, we can calculate the approximate number of grains of sand per square meter:
Number of grains of sand per square meter ≈ 2600 / 50.2656
≈ 51.7479
Therefore, there are approximately 51.7479 grains of sand on each square meter of the sphere's surface.