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
