The circumference of the base of a cylinder is 16π centimeters. The height of the cylinder is 10 centimeters.What is the surface area of the cylinder?
circumf = 16π
2πr = 16π
r = 8
SA of the cylinder = 2 circles + a rectangle
= 2π(8^2) + 2π(8)(10) = .....
To find the surface area of a cylinder, we need to calculate the area of the two bases and the area of the curved surface.
1. Calculate the area of the bases:
The circumference of the base is given as 16π cm. The formula for the circumference of a circle is C = 2πr, where C is the circumference and r is the radius. Therefore, the radius of the base circle can be found by dividing the given circumference by 2π:
16π = 2πr
Dividing both sides by 2π, we get:
r = 16π / 2π = 8 cm
The formula for the area of a circle is A = πr^2, where A is the area of the circle and r is the radius. Therefore, the area of each base can be calculated as follows:
A = π(8 cm)^2
A = 64π cm^2
2. Calculate the area of the curved surface:
The formula for the curved surface area of a cylinder is A = 2πrh, where A is the curved surface area, r is the radius, and h is the height. Plugging in the given values, we get:
A = 2π(8 cm)(10 cm)
A = 160π cm^2
3. Calculate the total surface area:
The total surface area of a cylinder is the sum of the areas of the two bases and the curved surface area:
Total surface area = 2(base area) + curved surface area
Total surface area = 2(64π cm^2) + 160π cm^2
Total surface area = 128π cm^2 + 160π cm^2
Total surface area = 288π cm^2
Therefore, the surface area of the cylinder is 288π square centimeters.
To find the surface area of a cylinder, you need to calculate the areas of the two bases and the lateral surface area, then add them together.
First, let's find the area of the base. The circumference of the base is given as 16π centimeters, so we can use the formula for the circumference of a circle: 2πr, where r is the radius. We need to find the radius, so we can divide the circumference by 2π:
Circumference = 2πr
16π = 2πr
Simplifying this equation, we can cancel out the π on both sides:
16 = 2r
Now we can divide both sides by 2 to find the value of r:
r = 8
The radius of the base is 8 centimeters.
Next, let's calculate the area of the base using the formula for the area of a circle: πr^2.
Area of base = πr^2
Area of base = π(8)^2 = 64π
The area of one base is 64π square centimeters.
Next, let's calculate the lateral surface area of the cylinder. The lateral surface area is the area of the side of the cylinder, which can be calculated by multiplying the height of the cylinder by the circumference of the base:
Lateral Surface Area = height × circumference of base
Lateral Surface Area = 10 × 16π = 160π
The lateral surface area of the cylinder is 160π square centimeters.
Finally, we can calculate the surface area of the cylinder by adding the area of the two bases and the lateral surface area:
Surface Area = 2(area of base) + Lateral Surface Area
Surface Area = 2(64π) + 160π
Surface Area = 128π + 160π
Surface Area = 288π
The surface area of the cylinder is 288π square centimeters.