A right cylinder has a base diameter of 12 meters and a height of 16 meters. What is the approximate surface area? Use 3.14 for 𝝅.
A = 2πr^2 + 2πrh = 2πr(r+h)
To find the surface area of a right cylinder, we need to calculate the area of the two bases and the lateral surface area.
1. The area of each base can be found using the formula for the area of a circle: 𝜋𝑟², where 𝑟 is the radius.
Given the diameter of the base is 12 meters, we can find the radius by dividing the diameter by 2.
Radius = 12 / 2 = 6 meters
The area of each base = 𝜋(6)² = 36𝜋 square meters (using 3.14 for 𝜋)
2. The lateral surface area can be calculated using the formula for the lateral area of a cylinder: 2𝜋𝑟ℎ, where 𝑟 is the radius and ℎ is the height.
Lateral surface area = 2𝜋(6)(16) = 192𝜋 square meters (using 3.14 for 𝜋)
3. To get the total surface area, we add the areas of the two bases and the lateral surface area.
Total surface area = 2 × (area of each base) + (lateral surface area)
= 2 × 36𝜋 + 192𝜋
= 72𝜋 + 192𝜋
= 264𝜋 square meters
Since the question asks for an approximate surface area, we can calculate the value of 𝜋 and then substitute it in the equation:
Total surface area = 264 × 3.14
= 828.96 square meters
Therefore, the approximate surface area of the cylinder is approximately 828.96 square meters.
To find the surface area of a right cylinder, we need to calculate the sum of the areas of the curved surface and the two bases.
First, let's calculate the surface area of the curved surface (lateral area). The lateral area of a cylinder can be calculated using the formula:
Lateral Area = 2πrh
where π is the mathematical constant pi (approximately 3.14), r is the radius of the base, and h is the height of the cylinder.
Given that the base diameter is 12 meters, the radius (r) is half of the diameter, so r = 12 / 2 = 6 meters. The height (h) of the cylinder is given as 16 meters.
Plugging in these values into the formula, we get:
Lateral Area = 2 * 3.14 * 6 * 16
Lateral Area ≈ 602.88 square meters
Next, let's calculate the area of one base. The base of a cylinder is a circle, and its area is given by the formula:
Base Area = πr^2
Using the radius (r) of 6 meters, we can calculate the area of one base:
Base Area = 3.14 * 6^2
Base Area ≈ 113.04 square meters
Since a cylinder has two bases, the combined surface area of both bases is given by:
Base Surface Area = 2 * Base Area
Base Surface Area ≈ 2 * 113.04
Base Surface Area ≈ 226.08 square meters
To find the total surface area, we sum the lateral area and the base surface area:
Total Surface Area = Lateral Area + Base Surface Area
Total Surface Area ≈ 602.88 + 226.08
Total Surface Area ≈ 828.96 square meters
Therefore, the approximate surface area of the given right cylinder is approximately 828.96 square meters.
d/2 = r
Cylinder Surface Area = 2 π r^2 h
I'll let you do the calculations.