What is the Surface Area of a Cylinder Dont Memorise

👁 1 مشاهدة

What is the Surface Area of a Cylinder Dont Memorise

Sri Chaitanya Academy NEET · ⏱ 3:08 · 510.9K مشاهدة · 11 years ago

📺 شاهد كل صفحات قناة "Sri Chaitanya Academy NEET"

النص الكامل للفيديو

Understanding how the surface area of cylinder is derived is very interesting. Look at this cylinder. It has two blue circular ends, one on top and one at the bottom. Analyze the figure. As we know the area of circle, we can easily find the surface area of the top and the bottom circular ends. But the important question is how do we find the surface area of this curved surface? Let's zoom out bit. First, let's separate the circular ends. This is the top one and this is the one at the bottom. To understand the curved surface, we cut it open vertically which will make it look like this. We just cut the surface vertically. When this is opened up further, it will look like rectangle. There are few questions we need to ask ourselves here. First, what is the length of the rectangle? And second, what is its breadth? If you look carefully, you will notice that the length of this rectangle is actually the circumference of the circular base because all we did was pull this open. What about its breath? Its breadth is the height of the cylinder. Let's assume the height of the cylinder is and the radius of the circular base is So the breadth will be and the length will be 2 pi Don't forget the area of this rectangle will be the curved surface area. But we need to find the total surface area of this cylinder. The surface area will be the sum of all these three surfaces. Two circles and the curved surface which is the rectangle. The area of the circular base is r². Since there are two equal circles, we write r² + r². This covers the surface area of the top and the bottom surfaces. And the area of this rectangle will be length multiplied by breadth which will be 2 * This 2 pi rh is actually the curved surface area of the cylinder. Adding these like terms we get 2 pi r² and we write 2 pi rh as is. 2 pi is common to both the terms. So we write the final formula as 2i * + If we are given the radius of the base and the height of the cylinder using this formula we can find out its total surface area.