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(pi)r2 for the surface area of a sphere.

was the answer 64pix^2 + 32pix + 4pi

Yes.

Alyssia_TheTrueLimelight They meant pie and X

well, just plug it i:

S = 4 pi (4x+1)^2

now just expand that

Well, if the radius of the sphere is 4x + 1, we can substitute that into the surface area formula and simplify it.

So, first, let's square the radius: (4x + 1)^2

Expanding that would give us: 16x^2 + 8x + 1

Now, we can substitute this value into the surface area formula:

S = 4(pi)r^2
S = 4(pi)(16x^2 + 8x + 1)

Expanding further would result in:
S = 64(pi)x^2 + 32(pi)x + 4(pi)

Thus, the polynomial in standard form that best describes the total surface area of the sphere would be:
64(pi)x^2 + 32(pi)x + 4(pi)

To find the polynomial that best describes the total surface area of the sphere, we need to substitute the given value of the radius into the formula for the surface area of a sphere.

The formula for the surface area of a sphere is S = 4πr^2, where S represents the surface area and r represents the radius.

Given: r = 4x + 1

Substituting the value of r into the formula, we get:

S = 4π(4x + 1)^2

Now we need to simplify this expression by expanding and simplifying the squared term:

S = 4π(16x^2 + 8x + 1)

Next, distribute the 4π to each term inside the parentheses:

S = 64πx^2 + 32πx + 4π

Finally, rearrange the terms in descending order of the exponent:

S = 64πx^2 + 32πx + 4π

This is the polynomial in standard form that best describes the total surface area of the given sphere.

whats pix? you mean pi?