Use 3.14 as pi. Lionel wants to paint a cylindrical hollow plastic pipe with a radius of 4 metres and a length of 20 metres. a. Determine the surface area to be painted.
The formula for the surface area of a cylinder is:
2(pi)(r)(h) + 2(pi)(r^2)
Where:
pi = 3.14
r = radius = 4 metres
h = length = 20 metres
Substituting the values, we get:
2(3.14)(4)(20) + 2(3.14)(4^2)
251.2 + 100.48
351.68
Therefore, Lionel needs to paint a surface area of approximately 351.68 square metres.
To determine the surface area to be painted, we need to calculate the area of the curved surface of the cylinder and the two circular faces.
1. Area of the curved surface:
The curved surface area of a cylinder is given by the formula: 2 * pi * radius * height, where pi is the mathematical constant approximately equal to 3.14, radius is the radius of the cylinder, and height is the length of the cylinder.
Using the given values, we can calculate the curved surface area as:
CSA = 2 * 3.14 * 4 * 20
= 502.4 square meters
2. Area of the circular faces:
The area of a circle is given by the formula: pi * radius^2.
Using the given values, we can calculate the area of one circular face as:
Circular Face Area = 3.14 * (4^2)
= 3.14 * 16
= 50.24 square meters
Since there are two circular faces, the total area of the two circular faces is:
Total Circular Face Area = 2 * 50.24
= 100.48 square meters
3. Total surface area:
The total surface area to be painted is the sum of the curved surface area and the total circular face area.
Total Surface Area = CSA + Total Circular Face Area
= 502.4 + 100.48
= 602.88 square meters
Therefore, the surface area to be painted is approximately 602.88 square meters.