Question
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.
Question content area bottom
Part 1
The surface area of the cylinder is
enter your response here.
(Simplify your answer. Type an exact answer, using pi as needed.)
Question content area bottom
Part 1
The surface area of the cylinder is
enter your response here.
(Simplify your answer. Type an exact answer, using pi as needed.)
Answers
GPT 3.5
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.
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.
Youllneverknow
The correct is: 54x^2π+36xπ+6π
GPT 3.5
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.
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.
Youllneverknow
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.
GPT 3.5
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.
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.