Use the diagram of the cylinder to answer the question. Use 3.14 for and round to the nearest tenth.
8 in.
8 in.
3. Find the surface area of the cylinder.
O 2009.6 in.²
O 401.9 in.²
O 803.8 in.²
O 602.9 in.²
803.8 in.²
To find the surface area of a cylinder, we need to add the areas of the two bases and the lateral surface area. The formula for the surface area of a cylinder is:
Surface Area = 2πr² + 2πrh
First, let's find the radius of the cylinder. We have the diameter, which is 8 inches. The radius is half of the diameter, so the radius is 8/2 = 4 inches.
Now, let's find the area of each base. The formula for the area of a circle is:
Area of base = πr²
Substituting the radius we found earlier, the area of each base is:
Area of base = 3.14 x (4)² = 3.14 x 16 = 50.24 in²
Next, we need to find the height of the cylinder. However, it is not provided in the given information. So, we cannot find the exact surface area of the cylinder.
Therefore, none of the options provided (2009.6 in.², 401.9 in.², 803.8 in.², 602.9 in.²) is correct without knowing the height of the cylinder.
To find the surface area of a cylinder, you need to calculate the sum of the areas of the two circular bases and the curved surface area.
First, let's find the area of the circular bases. The formula for the area of a circle is A = πr², where A is the area and r is the radius.
Given that the radius of the cylinder is 8 inches, we can calculate the area of each base using the formula:
A_base = π(8 in)²
A_base = 64π in²
Next, let's find the curved surface area. The formula for the lateral or curved surface area of a cylinder is A_lateral = 2πrh, where r is the radius and h is the height.
Since the height of the cylinder is also 8 inches, we can calculate the curved surface area using the formula:
A_lateral = 2π(8 in)(8 in)
A_lateral = 128π in²
Now, let's add up the areas of the bases and the curved surface area to find the total surface area of the cylinder:
A_total = A_base + A_base + A_lateral.
A_total = 64π + 64π + 128π
A_total = 256π in².
To round the answer to the nearest tenth, we can use the approximate value of π as 3.14:
A_total = 256(3.14) in²
A_total ≈ 803.8 in².
Therefore, the surface area of the cylinder is approximately 803.8 in².