direct variation
the surface area of a sphere varies directly as the square of the radius. if the surface area of a sphere is 36 pi meters squared when the radius is 3 meters, what is the surface area of a sphere with a radius of 6 meters?
S=k*r^2
solve for k first.
To solve for the constant of variation (k), we can use the given information that the surface area of the sphere is 36π when the radius is 3 meters.
Using the direct variation equation S = k * r^2, we can substitute the given values into the equation:
36π = k * 3^2
36π = k * 9
Now, we can solve for k by dividing both sides of the equation by 9:
k = (36π) / 9
k = 4π
Therefore, the constant of variation is 4π.
Now that we have the value of k, we can use it to find the surface area of the sphere with a radius of 6 meters by substituting it back into the direct variation equation:
S = (4π) * 6^2
S = 4π * 36
S = 144π
Hence, the surface area of the sphere with a radius of 6 meters is 144π square meters.