Answer:
18.62π square inches
Explanation:
To find the surface area of the cylinder, we need to find the area of each of its components and add them together. We can use the net of the cylinder to visualize its components and dimensions.
First, let's find the area of the top and bottom circles. We know the diameter of each circle is 3.8 inches, so the radius is half of that, or 1.9 inches. The formula for the area of a circle is A = πr^2, so:
A(top and bottom circles) = 2π(1.9 in)^2
= 2π(3.61 in^2)
= 7.22π in^2
Next, let's find the area of the curved surface of the cylinder. The height of the cylinder is labeled as 3 inches, which is also the height of the rectangle in the net. The length of the rectangle is the circumference of one of the circles, which is πd (where d is the diameter). So:
length of rectangle = π(3.8 in) = 11.96 in
The formula for the area of the curved surface of a cylinder is A = 2πrh, where r is the radius and h is the height. We can use the radius we found earlier and the height of 3 inches to calculate the area of the curved surface:
A(curved surface) = 2π(1.9 in)(3 in)
= 11.4π in^2
Finally, we can add the areas of the top and bottom circles and the curved surface to get the total surface area of the cylinder:
Total surface area = A(top and bottom circles) + A(curved surface)
= 7.22π in^2 + 11.4π in^2
= 18.62π in^2
Therefore, the surface area of the cylinder in terms of π is 18.62π square inches.