Determine the surface area of a cylinder whose height is 2m and whose base has an area of 9 pi m square?
http://www.math.com/tables/geometry/surfareas.htm
To determine the surface area of a cylinder, you need to calculate the sum of the areas of its curved surface (lateral surface area) and its two circular bases.
The formula for the lateral surface area of a cylinder is:
Lateral Surface Area = 2πrh
where 'r' is the radius of the base and 'h' is the height of the cylinder.
Given that the height of the cylinder is 2m, we are provided with half of the information needed to calculate the lateral surface area. However, we need to find the radius of the base to proceed.
The area of a circle can be calculated using the formula:
Area = πr^2
Given that the base has an area of 9π square meters, we can set up the equation:
9π = πr^2
Dividing both sides of the equation by π, we get:
9 = r^2
Taking the square root of both sides, we find that:
r = 3 meters
Now that we know the radius 'r' and the height 'h', we can calculate the lateral surface area:
Lateral Surface Area = 2πrh
Lateral Surface Area = 2π(3)(2)
Lateral Surface Area = 12π square meters
To find the total surface area of the cylinder, we need to add the areas of the two bases. The formula for the area of a circle (base) is the same as we used above, so each base has an area of 9π square meters.
Total Surface Area = Lateral Surface Area + 2(Base Area)
Total Surface Area = 12π + 2(9π)
Total Surface Area = 12π + 18π
Total Surface Area = 30π square meters
Therefore, the surface area of the given cylinder with a height of 2m and a base area of 9π square meters is 30π square meters.