Find The Surface Area Of Cylinders Quiz for students

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A cylinder is a basic three-dimensional shape which consists of some finite number of circles placed one over the other. On a 2d representation, from one of the view, the cylinder looks like a rectangle whose breadth is equivalent to the diameter of the circle and the length is the height of the cylinder. The cylinder has two areas which are curved surface area and the other is the areas of the two base circles. In this quiz, the child has to find out the area of the cylinder using the formulas that he or she has learned and needs to be quick to answer so that there won’t be any sign of confusion at the end.

What is surface area and how to find it for cylindrical shape?

The surface area of a cylinder is the total area of the outside surface of the cylinder. It’s a measure of how much area the outside of the cylinder takes up. To find the surface area of a cylinder, we need to know the radius of the circular base (the distance from the center of the circle to the edge) and the height of the cylinder.

There are a few different formulas we can use to find the surface area of a cylinder, depending on what information we have. Let’s start by looking at the most common formula:

Surface area = 2πr^2 + 2πrh

In this formula, “r” is the radius of the circular base and “h” is the height of the cylinder. “π” is a special number in math that stands for about 3.14.

To use this formula, we just need to plug in the values for “r” and “h.” Let’s say we have a cylinder with a radius of 3 and a height of 5. To find the surface area of the cylinder, we just need to plug these numbers into the formula:

Surface area = 2π x 3^2 + 2π x 3 x 5 Surface area = 18π + 30π Surface area = 48π

The surface area of a cylinder is usually measured in square units. So in this case, the surface area of the cylinder is about 150.7 square units.

Another way to find the surface area of a cylinder is to think about the cylinder as being made up of two circles and a rectangle. The two circles are the top and bottom of the cylinder, and the rectangle is the side of the cylinder.

To find the surface area of the cylinder using this method, we just need to find the area of each of the two circles and the rectangle, and then add them together.

To find the area of the two circles, we can use the formula for the area of a circle:

Area = πr^2

In this formula, “r” is the radius of the circle. So if the radius of the circles is 3, the area of each circle would be:

Area = π x 3^2 Area = 9π

To find the area of the rectangle, we just need to multiply the length by the width. The length of the rectangle is the same as the height of the cylinder, which is 5 in this case. The width of the rectangle is the circumference of the circle, which is 2πr. So if the radius of the circle is 3, the width of the rectangle would be:

Width = 2π x 3 Width = 6π

To find the area of the rectangle, we just need to multiply the length and the width:

Area = 5 x 6π Area = 30π

To find the surface area of the cylinder, we just need to add up the area of the two circles and the rectangle:

Surface area = 9π + 9π + 30π Surface area = 48π

This gives us the same result as before: the surface area of the cylinder is about 150.7 square units.

It might seem confusing at first to think about the surface area of a cylinder in terms of circles and rectangles, but it can be a helpful way to visualize the different parts of the cylinder and understand how they all contribute to the total surface area.

Overall, finding the surface area of a cylinder is all about understanding the different parts of the cylinder and how they all fit together.