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.
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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