A sphere has a radius of 7𝑥 + 7. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula 𝑆 = 4𝜋𝑟^2 for the surface area of a sphere.

a. 196𝜋𝑥^2 − 392𝜋𝑥 + 196𝜋
b. 196𝜋𝑥^2 + 392𝜋𝑥 + 196𝜋
c. 196𝜋𝑥^2 − 392𝜋𝑥 − 196𝜋
d. 196𝜋𝑥^2 − 3926𝜋𝑥 − 196𝜋

1 answer

A = 4 π r²

A = 4 π ( 7 x + 7 )² =

4 π [ ( 7 x )² + 2 ∙ 7 x ∙ 7 + 7² ] =

4 π ( 49 x² + 98 x + 49 ) =

4 π ∙ 49 x² + 4 π ∙ 98 x + 4 π ∙ 49 =

196 π x² + 392 π x + 196 π

Answer b