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? The choices are:
2pi(3x^2 + 10x - 8)
2pi(12x^2 + 7x - 2)
2pi(12x^2 - 2x + 13)
2pi(12x^2 - 5x - 2)
Please help me in setting this up and solving. Thanks
1.A
2.D
3.B
4.D
5.C
surface area = 2pi (r^2 + rh)(it is the formula)
So, we just plug it in.
ignoring the 2 pi, we see that r^2 = (3x-2)^2 = 9x^2-12x+4
r*h = (3x-2)(x+3)
Then we get for rh = 3x^2-2x+9x-6 =
3x^2 +7x-6.
We add these together to get 12x^2 -5x-2
multiply by 2pi we get
2pi(12x^2-5x-2)
That is the answer and thus it is D
To find the surface area of a cylinder, we need to find the areas of the two circular bases and the lateral surface area.
The formula for the surface area of a cylinder is:
Surface Area = 2πr² + 2πrh,
where r is the radius and h is the height.
Given:
Radius (r) = 3x - 2 cm,
Height (h) = x + 3 cm.
Substituting these values into the formula, we get:
Surface Area = 2π(3x - 2)² + 2π(3x - 2)(x + 3).
Now, let's simplify the equation:
Surface Area = 2π(9x² - 12x + 4) + 2π(3x² + 7x - 6).
Surface Area = 2π(9x² - 12x + 4 + 3x² + 7x - 6).
Surface Area = 2π(12x² - 5x - 2).
So, the correct answer is 2π(12x² - 5x - 2).
To find the surface area of a cylinder, we need to calculate the sum of the areas of both the circular bases and the lateral surface area.
Let's start by finding the area of one circular base. The area of a circle is given by the formula A = πr^2, where r represents the radius. In this case, the radius of the cylinder is 3x - 2 cm, so the area of one base is:
A1 = π(3x - 2)^2
Next, we need to calculate the lateral surface area. The lateral surface area of a cylinder is given by the formula A = 2πrh, where r is the radius, and h is the height. In this case, the radius is 3x - 2 cm, and the height is x + 3 cm, so the lateral surface area is:
A2 = 2π(3x - 2)(x + 3)
Finally, we add the area of the two circular bases and the lateral surface area to obtain the total surface area of the cylinder:
Total surface area = A1 + A2 = π(3x - 2)^2 + 2π(3x - 2)(x + 3)
Now we can simplify this expression:
Total surface area = π(9x^2 - 12x + 4) + 2π(3x^2 + 7x - 6)
Expanding and grouping like terms, we get:
Total surface area = π(9x^2 - 12x + 4 + 6x^2 + 14x - 12)
Simplifying further, we have:
Total surface area = π(15x^2 + 2x - 8)
Comparing this expression to the given choices, we can see that the correct option is 2π(15x^2 + 2x - 8).