A sphere has a radius of 4x + 4. Which polynomial in standard form best describes the total surface area of the sphere? Use the formula S = 4r2 for the surface area of a sphere.

Question

anonymous · Answer

The surface area is $S = 4\pi r^2$ as you are given and you know that the radius is $r = 4x+4$.  If you substitute that into the equation and simplify what do you get?
$$S = 4\pi(4x+4)^2=\cdots $$

anonymous · Answer

A. 64pix^2 + 128pix + 64pi
B. 64pix^2 – 128pix + 64pi
C. 64pix^2 + 128pix – 64pi
D. 64pix^2 – 128pix – 64pi

anonymous · Answer

I am not going to tell you the answer.  Please attempt it for yourself.

zehanz · Answer

You could save a little on the calculations by factoring out 4:

S=4π(4x+4)²=4π((4(x+1))²=4π16(x+1)²=64π(x+1)²=...

zehanz · Answer

@yakeyglee: don't be too harsh ;)

anonymous · Answer

I just need help ! I don't understand how to do it

anonymous · Answer

I'm new to this, I just created me an account like really

anonymous · Answer

What is not clear about our explanations?  They are guiding you to the answer.

zehanz · Answer

AFAIK, you now have 64π(x+1)², so first expand (x+1)²=(x+1)(x+1)=...

YOu must have learned how to do that (FOIL?)

anonymous · Answer

Can you just please give me the answer?

annipuppi · Answer

I have this same question on my homework... I'm really confused on it. so far after reading this I have 64pi(x^2+2x+2) am I doing it right so far? What do I do next? @yakeyglee @ZeHanz

zehanz · Answer

You're doing fine!
Now you just have to expand the brackets (use the distributive property), so multiply 64pi with x², with 2x and with 2...

annipuppi · Answer

so 64pix^2*128x*128?

zehanz · Answer

That would be 64pi(x^2+2x+1) = 64pix^2+128pix+64pi