Total Surface area is the second branch of the main topic area. Which means the measurement of extension of the outer part of the solid completely.Whereas the curved surface-area is the measurement of extension of only the curved part of the solid.
To understand more precisely, let us consider the three shapes namely cone, cylinder and sphere.
First,let us consider a right circular solid cylinder.If we need to find the curved surface-area, we need to find the measurement of extension of only the curved portion. More clearly, the measurement of extension that is curved,which exclude the extension of the top portion and bottom portion (there are two circles at the top and base). Curved surface-area means the measurement of extension,excluding the areas of the two circles where one is at the top and other one is at the bottom(base). But if we need to find the total surface-area, we have to include the areas of two circles where one is at the bottom and another one is at the top.
Second, let us consider a right circular solid cone. Here we do not have anything at the top like we have a circle at the top portion of the cylinder.We have a circle only at the base (bottom).
So if we find curved surface-area, we will find only the curved portion of the cone and we will never include the area of the circle at the base. But,if we want to find the total surface-area,along with curved surface-area, we need to include the area of the circle at the bottom(base)
Third, let us consider the shape sphere. In a cylinder, we are having two circles where one is the top potion and another one is at the bottom.So when we need to find the total surface area, with the curved surface-area, we have to include the areas of two circles. In the shape cone, we do not have anything at the top. We will have only one vertex. So when we want to find the total surface area, with the curved surface-area, we include the area of the circle which is at the base(bottom). In the shape sphere, we do not have a circle or any other shape at both top and bottom. So there is no difference between curved surface-area and total surface-area. Because even if we use the word curved-surface-area, it means the curved part of the solid that is which covers the entire part of the solid.
In sphere, both the terms total surface-area and curved surface-area means same .
Hemisphere:
But in the hemisphere,curved surface-area and total surface-area are different.Because in the shape hemisphere, we will have a circle at the top.(When it is in the position of the bowl). Curved surface-area measures the extension of only the part which exclude the extension of the circle at the top.But, if we need to find the total surface area, with curved surface-area, we have to include the extension of the circle at the top.
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