The radius of a cylindrical gift box is (4x+3) inches, the height of the gift box is twice the radius. what is the surface area of the cylinder? write your answer as a polynomial in standard from. someone me : [

So how i find surface area is separating all the sides of the figure, finding all their individual areas, then add all the areas together. So here's how to do it.
There are two circles and one rectangle in a cylinder. The two circles are the top and bottom, and the rectangle is the side of the cylinder.
So first let's find the area of the circles.
The equation for the area of a circle is A=3.14 (aka pi) * r^2
Now we are given the radius: 4x+3
Now in order to get the area, we have to square it so:
(4x+3)(4x+3)
Distribute
16x^2+12x+12x+9
Simplify like terms
16x^2+12x+9
Now that we have r^2, we have to multiply by our. Idk how your specific teacher wants it left, so I'll deal with it later, well just keep it Unsimplified for now.
So the area of ONE of the circles is 3.14*(16x^2+12x+9)
But we have TWO circles, one on top and bottom, as I stated previously.
So we have to multiply it by 2 to get both circles. I'm just gonna distribute it into the parentheses, leaving the pi alone.
3.14*(32x^2+24x+18)
Now that we have the circles, we need the area of the wrapped around rectangle. In order to find the dimensions of the rectangle, we need to find the height of the cylinder, and the width of the rectangle. Now it says the height of it is twice the radius, so we can just multiply the radius by 2, leaving (8x+6) as the height.
In order to find the width, we need to find the circumference of the circle, to see how much the rectangle had to wrap around.
Now the equation of the circumference of a circle is C=3.14*2r
Now put the value of the radius into the equation, leaving us with
C=3.14*(8x+6)
Now that we have the height and the width, we can find the area of the rectangle.
A=(8x+6)*(3.14)*(8x+6)
Again we are going to leave he pi alone until I clarify with u how ur teacher wants it, so we with multiply out the (8x+6)'s
A=(3.14)*(64x^2+48x+48x+36)
Simplify it down even further
A=(3.14)*(64x^2+96x+36)
Now that's the area of the rectangle. Now that we calculated both of the areas, we just need to add hem together.
(3.14)*(64x^2+96x+36)+(3.14)*(32x^2+24x+18)
So the total surface area equals that, but we are have to simplify it further.
Let's remove 3.14 from both equations by distributing it out.
(3.14)((64x^2+96x+36)+(32x^2+24x+18))
Now let's simplify like terms
(3.14)(96x^2+120x+54))
And there we are, all we need to do is add the units.
(3.14)(96x^2+120x+54))in^2
Voila. Feel free to ask for any further questions.

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