The radius of a cylinder is 3x – 2 cm. The height of the cylinder is x + 3 cm. What is the surface area of the cylinder? Use the formula A = 2r2 + 2rh.%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A2(3x2 + 10x – 8)%0D%0A2 Image with alt text: symbol pi (3 x 2 + 10 x – 8)%0D%0A%0D%0A%0D%0AImage with alt text: 2 pi left-parenthesis 12 x squared plus 7x minus 2 right-parenthesis%0D%0A%0D%0A%0D%0AImage with alt text: 2 pi left-parenthesis 12 x squared minus 2x plus 13 right-parenthesis
To find the surface area of the cylinder, we need to substitute the given values into the formula A = 2r^2 + 2rh.
The radius of the cylinder is 3x - 2 cm, so we replace 'r' with 3x - 2 in the formula.
The height of the cylinder is x + 3 cm, so we replace 'h' with x + 3 in the formula.
A = 2(3x - 2)^2 + 2(3x - 2)(x + 3)
Simplifying the formula, we get:
A = 2(9x^2 - 12x + 4) + 2(3x^2 + 7x - 6)
A = 18x^2 - 24x + 8 + 6x^2 + 14x - 12
A = 24x^2 - 10x - 4
Therefore, the surface area of the cylinder is 24x^2 - 10x - 4.
No 3.14157 ?????
I apologize for the confusion. The formula for the surface area of a cylinder is A = 2πr^2 + 2πrh.
Let's substitute the given values into the formula. The radius of the cylinder is 3x - 2 cm, so we replace 'r' with 3x - 2 in the formula. The height of the cylinder is x + 3 cm, so we replace 'h' with x + 3 in the formula.
A = 2π(3x - 2)^2 + 2π(3x - 2)(x + 3)
Simplifying the formula, we get:
A = 2π(9x^2 - 12x + 4) + 2π(3x^2 + 7x - 6)
A = 18πx^2 - 24πx + 8π + 6πx^2 + 14πx - 12π
A = 24πx^2 - 10πx - 4π
Therefore, the surface area of the cylinder is 24πx^2 - 10πx - 4π.
To find the surface area of the cylinder, we'll use the formula A = 2πr² + 2πrh, where A represents the surface area, r is the radius of the base, h is the height, and π is a mathematical constant that approximates to 3.14159.
In this case, the radius of the cylinder is given as 3x - 2 cm, and the height is x + 3 cm. We will substitute these values into the formula.
Step 1: Calculate the surface area of the bases.
The formula for the area of a circle is A = πr². Since the cylinder has two bases, the surface area contributed by the bases is 2πr².
Substitute the given radius (3x - 2 cm) into the formula:
Surface area of bases = 2π(3x - 2)²
Step 2: Calculate the surface area of the curved part.
The curved part of the cylinder's surface forms a rectangle when unrolled. The height of the rectangle is equal to the height of the cylinder (x + 3 cm), and the length of the rectangle is equal to the circumference of the base (2πr).
Substitute the given radius (3x - 2 cm) and height (x + 3 cm) into the formula:
Surface area of curved part = 2π(3x - 2)(x + 3)
Step 3: Add the surface areas of the bases and curved part.
Total surface area = Surface area of bases + Surface area of curved part
Total surface area = 2π(3x - 2)² + 2π(3x - 2)(x + 3)
Simplifying further is necessary to obtain the final expression for the surface area.