12. A sphere has a radius of 4x + 1. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4 r2 for the surface area of a sphere. (1 point)
64 x2 + 32 x + 4
64 x2 + 16 x + 4 *my answer
4 x2 + 32 x + 64
4 x2 + 4
4(4x+1)^2 = 4(16x^2+8x+1)
Better double-check your answer.
Thank you, and found it was the first one.
We have a winner!
To find the total surface area of a sphere with a given radius, we can use the formula S = 4πr^2, where S is the surface area and r is the radius. In this case, the given radius of the sphere is 4x + 1.
To determine the polynomial that best describes the total surface area, we need to substitute the given radius into the surface area formula.
Substituting 4x + 1 into the formula, we get:
S = 4π(4x + 1)^2
Expanding the square, we have:
S = 4π(16x^2 + 8x + 1)
Distributing 4π to each term, we get:
S = 64πx^2 + 32πx + 4π
Since we are looking for the polynomial in standard form without using π as a coefficient, we can disregard it and simplify the expression by multiplying each term by π:
S = 64x^2 + 32x + 4
Therefore, the polynomial in standard form that best describes the total surface area of the sphere with a radius of 4x + 1 is 64x^2 + 32x + 4.
So the correct answer is "64 x^2 + 32 x + 4".