Question

The radius of a cylindrical gift box is ​(4x + 1​) 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:

S = 128πx² + 64πx + 8π

Step-by-step explanation:

Suraface area of a cylinder is given by:

S = 2πrh + 2πr²

We know that the height is 3 times as big as the radius, hence:

h = 3r

so we can plug in the new h value and rewrite the S equation as:

S = 2πrh + 2πr²

S = 2πr(3r) + 2πr²

S = 6πr² + 2πr²

S = 8πr²

We're given in the question that the radius is ​(4x + 1​) inches, so plug that into r.

Given: r = 4x + 1​

Therefore,

S = 8πr²

S = 8π(4x + 1​)²

S = 8π(16x²+8x+1)

S = 128πx² + 64πx + 8π

Answer 2

Answer:

The answer to your question is 128πx² + 64πx + 8π

Step-by-step explanation:

Data

radius = (4x + 1)

height = 3(4x + 1)

Formula

Area = 2πrh + 2πr²

Substitution

Area = 2π(4x + 1)(3)(4x + 1) + 2π(4x + 1)

Simplification

Area = 6π(4x + 1)² + 2π(4x + 1)²

Area = 6π(16x² + 8x + 1) + 2π(16x² + 8x + 1)²

Area = 96πx² + 48πx + 6π + 32πx² + 16πx + 2π

Area = 128πx² + 64πx + 8π