What is the surface area of a right circular cylinder with base circle of radius of 5m and height of the cylinder 10m?
The formula for the surface area of a right circular cylinder is;
SA = 2*pi*r*h + 2*pi*r^2
To find the surface area of a right circular cylinder, you need to calculate the area of the two circular bases and the lateral surface area. Here's how you can do it:
1. Calculate the area of the two circular bases:
The formula for the area of a circle is A = πr^2, where A represents area and r represents the radius of the circle.
In this case, the base circle has a radius of 5m, so the area of each circular base is A = π(5^2) = 25π square meters.
2. Calculate the lateral surface area:
The lateral surface area represents the curved portion of the cylinder, which can be found by multiplying the circumference of the base circle by the height of the cylinder.
The formula for the circumference of a circle is C = 2πr, where C represents circumference and r represents the radius of the circle.
In this case, the circumference of the base circle is C = 2π(5) = 10π meters.
Now multiply the circumference of the base circle by the height of the cylinder: Lateral Surface Area = 10π * 10 = 100π square meters.
3. Add the areas of the two circular bases and the lateral surface area to find the total surface area: Total Surface Area = 2(25π) + 100π = 50π + 100π = 150π square meters.
Therefore, the surface area of the given right circular cylinder is 150π square meters.