Question

The radius of a cylindrical gift box is ​(3x+1​) 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 form.

Answer 1

Answer:

56πx² + 36πx + 6π square inches

Step-by-step explanation:

The radius of a cylindrical gift box is ​(3x+1​) 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 form.

The surface area of a cylinder is given as:

2πr(r + h)

The radius of a cylindrical gift box is ​(3x+1​) inches.

The height of the gift box is twice the radius = 2(3x + 1) inches

= 6x + 2 inches

The surface area of the cylinder is:

= 2 × π × 3x + 1( 3x + 1 + 6x + 2) square inches

= 2 × π × 3x + 1(9x + 3) square inches

= 2π × 3x + 1(9x + 3) square inches

= 6πx + 2π( 9x + 3) square inches

= 6πx (9x + 3) + 2π( 9x + 3) square inches

= 56πx² + 18πx + 18πx + 6π square inches

= 56πx² + 36πx + 6π square inches

The surface area of the​ cylinder is 56πx² + 36πx + 6π square inches