a sphere has a radius of 2x+5. which polynomial in standard form best describes the total surface area of the sphere? use the formula S=4pie r^2for the surface area of a sphere
To find the surface area of a sphere, we can use the formula S = 4πr^2, where r is the radius of the sphere. In this case, the given radius is 2x + 5.
So, the surface area of the sphere can be calculated as follows:
S = 4π(2x + 5)^2
Multiplying this out:
S = 4π(4x^2 + 20x + 25)
Simplifying further:
S = 16πx^2 + 80πx + 100π
Therefore, the polynomial in standard form that best describes the total surface area of the sphere is:
16πx^2 + 80πx + 100π