What is the surface area of a right circular cylinder with base circle of radius of 5m and height of the cylinder 10m?
Surface Area = 2(pi r^2) + (2 pi r)* h
To find the surface area of a right circular cylinder, you need to calculate the areas of the two base circles and the curved surface area.
1. Calculate the area of each base circle:
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
Given that the base circle has a radius of 5m, the area of each base circle would be:
A_base = π(5^2)
2. Calculate the curved surface area:
The curved surface area of a cylinder is given by the formula A_curved = 2πrh, where A_curved is the curved surface area, r is the radius of the base circle, and h is the height of the cylinder.
Given that the radius is 5m and the height is 10m, the curved surface area would be:
A_curved = 2π(5)(10)
3. Add up the areas of the two base circles and the curved surface area:
The total surface area (A_total) of a cylinder is the sum of the base areas and the curved surface area:
A_total = 2A_base + A_curved
Now, let's calculate the values:
1. Area of each base circle:
A_base = π(5^2) = 25π
2. Curved surface area:
A_curved = 2π(5)(10) = 100π
3. Total surface area:
A_total = 2A_base + A_curved
= 2(25π) + 100π
Therefore, the surface area of the right circular cylinder with a base circle of radius 5m and a height of 10m is 150π square meters.