The radius of a cylindrical gift box is (3x + 2) inches. The height of the gift box is twice the radius. What is the surface area of the cylinder?

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The radius of a cylindrical gift box is ​(3x+2​) inches. The height of the gift box is twice the radius. The surface area of the​ cylinder is 54πx² + 84πx + 32π square inches.

What is the surface area of a cylinder?

The surface area of a cylinder is given as:

2πr(r + h)

The radius of a cylindrical gift box is ​(3x+2​) inches. The height of the gift box is twice the radius.

We need to find the surface area of the​ cylinder.

The radius of a cylindrical gift box is ​(3x+2​) inches.

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

= 6x + 4 inches

The surface area of the cylinder is:

= 2 × π × (3x + 2)( 3x + 2 + 6x + 4) square inches

= 2 × π × (3x + 2)(9x + 8) square inches

= 6πx + 4π( 9x + 8) square inches

= 6πx (9x + 8) + 4π( 9x + 8) square inches

= 54πx² + 48πx + 36πx + 32π square inches

= 54πx² + 84πx + 32π square inches

Hence, The surface area of the​ cylinder is 54πx² + 84πx + 32π square inches.

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