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)r^2 for the surface area of a sphere.
16(pi)x^2 + 16(pi)
16(pi)x^2 + 48(pi)x + 16(pi)
36(pi)x^2 + 48(pi)x + 16(pi)
36(pi)x^2 + 24(pi)x + 16(pi)
36πx2+48πx+16π :)
SA = 4πr^2
= 4π(4x+1)^2
= 4π(16x^2 + 8x + 1)
= 64πr^2 + 32πx + 4π
None of the choices match this
Reiny, this is what I get too, but yes, it is none of the options:( Can you help me with one more?
nevermind, I got it:) Thank you
To find the total surface area of a sphere, we can use the formula S = 4(pi)r^2, where S represents the surface area and r represents the radius.
In this case, the radius of the sphere is given as 4x + 1. To find the total surface area, substitute the value of the radius into the formula.
S = 4(pi)(4x + 1)^2
Simplifying the expression (4x + 1)^2, we get:
S = 4(pi)(16x^2 + 8x + 1)
Expanding the expression, we multiply 4(pi) with each term inside the parentheses:
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 is:
64(pi)x^2 + 32(pi)x + 4(pi)
Therefore, the correct answer is 64(pi)x^2 + 32(pi)x + 4(pi).