i have to find the surface area of a cylinder with the height of 15 and the circumference of 4 to the nearest tenth of a square unit and cannot figure it out HELP PLEASE
the lateral surface area is just the circumference times the height.
So,
a = 4*15 = 60
if you have to include the ends, then that is additional 2πr^2, where r = 4/2π
To find the surface area of a cylinder, you need to calculate the sum of the areas of its two bases and its lateral surface.
First, let's find the area of one base of the cylinder. The base of a cylinder is a circle, and the formula to calculate the area of a circle is A = πr^2, where A is the area and r is the radius.
Since we know the circumference of the base is 4, we can use the formula C = 2πr to find the radius (r). Rearranging the formula, we have r = C / (2π). Substituting the given circumference, we get r = 4 / (2π) = 2 / π.
To find the area of one base, we can now substitute the radius into the area formula: A_base = π(2/π)^2 = π(4/π^2) = 4/π square units.
The next step is to find the lateral surface area of the cylinder. The formula for the lateral surface area of a cylinder is A_lateral = 2πrh, where r is the radius and h is the height of the cylinder.
Plugging in the values for radius (2/π) and height (15), we get A_lateral = 2π(2/π)(15) = 60 square units.
The total surface area of the cylinder is the sum of the areas of the bases and the lateral surface area: A_total = 2(A_base) + A_lateral = 2(4/π) + 60.
Calculating this expression will give you the surface area of the cylinder. Remember to round your answer to the nearest tenth since the question requires it.