A rectangular and two circular cut-outs of metal sheet of negligible thickness are used to make a closed cylinder. The rectangular cut-out ha a height of 18 cm. Each circular cut-out has a radius of 5.2 cm. Calculate in terms of area of π, the surface area of the cylinder.
To calculate the surface area of the cylinder, we need to find the areas of the individual components and then sum them together.
1. Base and Top: The base and top of the cylinder are both circles with a radius of 5.2 cm. The area of each circle can be calculated using the formula:
Area = π * radius^2
So, the area of one circular base = π * (5.2 cm)^2
2. Side: The side of the cylinder is formed by rolling the rectangular cut-out into a cylindrical shape. The length of the rectangular cut-out is equal to the circumference of the cylinder, which can be calculated using the formula:
Circumference = 2 * π * radius
So, the length of the rectangular cut-out is 2 * π * 5.2 cm.
The height of the rectangular cut-out is given as 18 cm, which becomes the height of the cylinder.
The area of the side can be calculated using the formula:
Area = length * height
So, the area of the side = (2 * π * 5.2 cm) * 18 cm
3. Surface Area: To get the total surface area of the cylinder, we sum up the areas of the base, top, and side:
Total Surface Area = 2 * Area of the base + Area of the side
So, Total Surface Area = 2 * (π * (5.2 cm)^2) + (2 * π * 5.2 cm) * 18 cm
Simplifying this expression will give us the surface area of the cylinder in terms of π.
assuming the rectangle is long enough to wrap around the cylinder,
a = πr^2 + πr^2 + 2πrh = 2πr(r+h)
Now just plug in r and h.