If you have read the cover of this worksheet and wondered if it was really true, then you are in luck because this worksheet can help you understand the surface area of prisms and cylinders. It helps to understand the surface area of all objects because we tend to consider the surface area of the largest object to be the largest part of an object.
In the worksheet, we have a cylinder and a prism being added together. In addition, we then have a length and a width of a circle and then we calculate the circumference of a cylinder from the circumference of the circle. What do we find when we do this?
First of all, we find that the area of the cylinder is greater than the area of the prism. That means the surface area of the cylinder is larger than the surface area of the prism. If we add up the areas of both the two shapes, we see that the surface area of the cylinder is greater than the surface area of the prism. We can also see that the area of the circle is greater than the area of the prism and the surface area of the circle is greater than the surface area of the cylinder.
The following question that will pop into your mind at this point is, “What is the surface area of the circle?” Well, if we add up the areas of the circles and the cylinders, we will find that the surface area of the cylinder is greater than the surface area of the circle. In addition, we find that the surface area of the circle is greater than the surface area of the prism.
We have just found that the surface area of the circle is greater than the surface area of the prism. If we repeat the same process as before and only subtract the surfaces from each other, we will get the surface area of the cylinder and the surface area of the prism. What do we find when we do this? We find that the surface area of the cylinder is less than the surface area of the prism.
In the worksheet, we have the surface area of the cylinder is less than the surface area of the prism. In order to find out why the surface area of the cylinder is less than the surface area of the prism, we need to figure out what is the radius of the cylinder. So now we know the radius of the cylinder and the surface area of the cylinder is greater than the surface area of the prism.
The next question that will pop into your mind is, “What is the surface area of the circle?” This is easier to answer than the previous question.
The surface area of the circle is equal to the area of the circle divided by the radius of the circle. In addition, we must then find out what is the surface area of the prism. In our worksheet, we have the area of the circle is equal to the area of the circle divided by the radius of the circle. We then need to find out what is the surface area of the prism.
