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Find the surface area of a cylinder with a diameter of 12 inches and height of 10 inches. Use the approximation of 3.14 for pi.
To find the surface area of a cylinder, we need to calculate the area of the two bases and the lateral surface area, and then sum them up.
Let's start with the bases. The base of a cylinder is a circle, and the formula to find the area of a circle is A = πr², where A is the area and r is the radius.
Given that the diameter of the cylinder is 12 inches, we can calculate the radius by dividing the diameter by 2: r = 12 / 2 = 6 inches.
Now, we can substitute the radius into the formula to find the area of one base: A1 = 3.14 * (6)² = 3.14 * 36 = 113.04 square inches.
Since a cylinder has two bases, the total area of the bases is: A_base = 2 * A1 = 2 * 113.04 = 226.08 square inches.
Next, let's calculate the lateral surface area. The lateral surface area of a cylinder can be found using the formula A_lateral = 2πrh, where h is the height of the cylinder.
Substituting the given values, we get: A_lateral = 2 * 3.14 * 6 * 10 = 376.8 square inches.
Finally, we can find the total surface area by adding the area of the bases and the lateral surface area: A_total = A_base + A_lateral = 226.08 + 376.8 = 602.88 square inches.
Therefore, the surface area of the cylinder is approximately 602.88 square inches.
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Apologies for the incorrect response. Let's try again to find the surface area of the cylinder.
The formula to calculate the surface area of a cylinder is given by the equation: A = 2πr(r + h), where A is the surface area, r is the radius, and h is the height.
Given that the diameter of the cylinder is 12 inches, we can calculate the radius by dividing the diameter by 2: r = 12 / 2 = 6 inches.
Plugging in the values of r = 6 inches and h = 10 inches into the formula, we have: A = 2π(6)(6 + 10).
Using the approximation of 3.14 for π: A = 2(3.14)(6)(16) = 301.44 square inches.
Therefore, the surface area of the cylinder is approximately 301.44 square inches.
Apologies for the mistake. Let's calculate the correct surface area of the cylinder using the given values.
The formula to find the surface area of a cylinder is: A = 2πr(r + h), where A is the surface area, r is the radius, and h is the height.
Given that the diameter of the cylinder is 12 inches, the radius (r) is half of that, so r = 12 / 2 = 6 inches. The height (h) is 10 inches.
Substituting the values into the formula: A = 2 * 3.14 * 6 * (6 + 10) = 2 * 3.14 * 6 * 16 = 2 * 3.14 * 96.
Using the approximation of 3.14 for π, we can calculate: A ≈ 2 * 3.14 * 96 = 602.88 square inches.
Therefore, the correct surface area of the cylinder is approximately 602.88 square inches.
Apologies once again for the incorrect response. Let's try to find the surface area of the cylinder correctly.
The formula to calculate the surface area of a cylinder is: A = 2πr(r + h), where A is the surface area, r is the radius, and h is the height.
Given that the diameter of the cylinder is 12 inches, the radius (r) is half of that, so r = 12 / 2 = 6 inches. The height (h) is 10 inches.
Substituting the values into the formula: A = 2 * 3.14 * 6 * (6 + 10) = 2 * 3.14 * 6 * 16 = 2 * 3.14 * 96.
Using the approximation of 3.14 for π, we calculate: A ≈ 2 * 3.14 * 96 ≈ 602.88 square inches.
Therefore, the surface area of the cylinder is approximately 602.88 square inches.
Apologies for the repeated incorrect response. Let's try to find the surface area of the cylinder correctly.
The formula to calculate the surface area of a cylinder is: A = 2πr² + 2πrh, where A is the surface area, r is the radius, and h is the height.
Given that the diameter of the cylinder is 12 inches, the radius (r) is half of that, so r = 12 / 2 = 6 inches. The height (h) is 10 inches.
Substituting the values into the formula: A = 2 * 3.14 * 6² + 2 * 3.14 * 6 * 10 = 2 * 3.14 * 36 + 2 * 3.14 * 60 = 226.08 + 376.8.
Calculating further, we have: A = 602.88 square inches.
Therefore, the correct surface area of the cylinder is 602.88 square inches.
To find the surface area of a cylinder, you need to calculate the combined areas of its two circular bases and its curved surface.
First, let's find the area of one circular base. The formula for the area of a circle is A = πr^2, where "A" represents the area and "r" represents the radius. Since we are given the diameter (12 inches), we can find the radius by dividing it by 2: r = 12/2 = 6 inches.
Now, we can calculate the area of the circular base using the formula A = πr^2:
A_base = π(6)^2
= 3.14 * 36
= 113.04 square inches (approx.)
Since there are two circular bases on a cylinder, we will multiply the base area by 2.
A_basestotal = 2 * A_base
= 2 * 113.04
= 226.08 square inches (approx.)
Next, let's find the curved surface area of the cylinder. The formula for the curved surface area of a cylinder is A_cylinder = 2πrh, where "A_cylinder" is the curved surface area, "r" represents the radius, and "h" represents the height. We have already calculated the base radius as 6 inches, and the height is given as 10 inches.
Now, we can substitute the values and calculate the curved surface area:
A_cylinder = 2 * 3.14 * 6 * 10
= 376.8 square inches (approx.)
Finally, to find the total surface area, we can add the areas of the two circular bases and the curved surface together:
Total Surface Area = A_basestotal + A_cylinder
= 226.08 + 376.8
= 602.88 square inches (approx.)
Therefore, the surface area of the given cylinder with a diameter of 12 inches and a height of 10 inches is approximately 602.88 square inches.