The radius of a cylindrical gift box is (3xplus1) 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.
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Part 1
The surface area of the cylinder is
enter your response here.
(Simplify your answer. Type an exact answer, using pi as needed.)
To find the surface area of a cylinder, we use the formula:
Surface Area = 2πr^2 + 2πrh
Given that the radius is (3x+1) inches, and the height is twice the radius, we can express the height as 2(3x+1) = 6x + 2 inches.
Therefore, the surface area of the cylinder is:
Surface Area = 2π(3x+1)^2 + 2π(3x+1)(6x+2)
Surface Area = 2π(9x^2 + 6x + 1) + 2π(18x^2 + 6x + 6)
Surface Area = 18πx^2 + 12πx + 2π + 36πx^2 + 12πx + 12π
Surface Area = 54πx^2 + 24πx + 14π
Therefore, the surface area of the cylinder is 54πx^2 + 24πx + 14π inches.
The correct is: 54x^2π+36xπ+6π
Surface Area = 2πr^2 + 2πrh
Surface Area = 2π(3x+1)^2 + 2π(3x+1)(6x+2)
Surface Area = 2π(9x^2 + 6x + 1) + 2π(18x^2 + 6x + 2)
Surface Area = 18πx^2 + 12πx + 2π + 36πx^2 + 12πx + 4π
Surface Area = 54πx^2 + 24πx + 6π
Therefore, the surface area of the cylinder is 54x^2π+36xπ+6π inches squared.
The radius of a cylindrical gift box is (4xplus1) 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.
Given that the radius of the cylindrical gift box is (4x + 1) inches and the height is twice the radius, the height can be expressed as 2(4x + 1) = 8x + 2 inches.
To find the surface area of the cylinder, we use the formula:
Surface Area = 2πr^2 + 2πrh
Substitute the values:
Surface Area = 2π(4x + 1)^2 + 2π(4x + 1)(8x + 2)
Surface Area = 2π(16x^2 + 8x + 1) + 2π(32x^2 + 8x + 2)
Surface Area = 32πx^2 + 16πx + 2π + 64πx^2 + 16πx + 4π
Surface Area = 96πx^2 + 32πx + 6π
Therefore, the surface area of the cylinder is 96x^2π + 32xπ + 6π inches squared.