Question

The radius of a cylindrical gift box is ​(4xplus1​) inches. The height of the gift box is three times the radius. What is the surface area of the​ cylinder? Write your answer as a polynomial in standard form.

Answer 1

Answer:

$(5x+1)\pi$

Step-by-step explanation:

Given:

The radius of a cylindrical gift box = $4x+1$

The height of the gift box is three times the radius.

Question asked:

What is the surface area of the​ cylinder ?

Solution:

The height of the gift box is three times the radius means,

$height = 3(4x+1)$

          $= 3\times4x+3\times1\\= 12x+3$

Now, surface area of the​ cylinder = $2\pi r(r+h)$

                                                        $=2\pi[4x+1](4x+1+12x+3)\\=8\pi x+2\pi(16x+4)\\=8\pi x+32\pi x+8\pi\\=40\pi x+8\pi\\=8\pi(5x+1) \ Taking \ common$

Therefore, surface area of the​ cylinder is $(5x+1)\pi$.