Find the surface area of a cylinder with a diameter of 12 inches and height of 10 inches.
To find the surface area of a cylinder, we need to calculate the surface area of the two bases and the lateral surface area.
The surface area of a base of a cylinder is given by the formula $\pi r^2$, where $r$ is the radius of the base.
The radius of the base is half of the diameter, so it is $12/2=6$ inches.
The lateral surface area of a cylinder is given by the formula $2\pi rh$, where $r$ is the radius of the base and $h$ is the height.
The surface area of the two bases is $2 \cdot \pi \cdot 6^2 = 2 \cdot 36 \cdot \pi = 72\pi$ square inches.
The lateral surface area is $2\pi \times 6 \times 10 = 120\pi$ square inches.
Therefore, the total surface area of the cylinder is $72\pi + 120\pi = 192\pi$ square inches.
Since the value of $\pi$ is approximately 3.14, the surface area of the cylinder is approximately $192\cdot3.14 \approx \boxed{602.88}$ square inches.
Use the approximation of 3.14 for pi.
The surface area of the cylinder is $192\cdot3.14\approx \boxed{603.36}$ square inches.
To find the surface area of a cylinder, you'll need to calculate the areas of its two bases and the area of its curved surface.
First, let's find the area of one of the bases. The base of a cylinder is a circle, and its area can be calculated using the formula:
Area of a circle = π * radius^2
The diameter of the cylinder is given as 12 inches, so the radius (r) is half of that, which is 6 inches. Therefore, the area (A1) of one base is:
A1 = π * 6^2
Next, let's find the curved surface area. The curved surface of a cylinder is like a rectangular shape that wraps around the circumference of the base. The height of the cylinder (h) is given as 10 inches, and the circumference of the base can be calculated using the diameter:
Circumference of a circle = π * diameter
So, the circumference is:
C = π * 12
To find the curved surface area (A2), multiply the circumference (C) by the height (h):
A2 = C * h = π * 12 * 10
Now, to find the total surface area (A_total) of the cylinder, add the areas of the two bases (A1) and the curved surface (A2):
A_total = 2 * A1 + A2
Substituting the values we've calculated, we have:
A_total = 2 * (π * 6^2) + (π * 12 * 10)
Simplifying further, we get:
A_total ≈ 2 * 113.04 + 376.99
A_total ≈ 226.08 + 376.99
A_total ≈ 603.07 square inches
Therefore, the surface area of the given cylinder is approximately 603.07 square inches.