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Surface Area of Joined Solids - Concept
Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school
Brian was a geometry teacher through the Teach for America program and started the geometry program at his school
Surface area is a two-dimensional property of a three-dimensional figure. When solids are joined together, such as a hemisphere on a cone, the surface area of the connecting circle is not included in the overall surface area - it is "hidden." Thus, to solve surface area of joined solids problems, determine which faces or bases are hidden and find the surface area of the remaining parts.
Once you know how to calculate the surface area of just about any polyhedron you're gong to apply it to different problems where you've got some joined surfaces. In this one you have a cone joined to a cylinder. So if we're to calculate the surface area of this polyhedron you're going to have to think about, well where the part is overlapped. Well we're going to start off with the lateral area of this cone, which I'm going to draw as a sector. Since thatÂ’s what it looks like if you unfold it. So we're going to say a lateral area of the cone, then you're going to add in not the base of the cone but the lateral area of the cylinder which is a rectangle. So I'm going to add in the lateral area of the cylinder and last you're going to add in the base of the cylinder which is a circle. So we'll say the base of the cylinder, the common mistake when you're trying to find the surface area is either adding in 2 circles because you see 2 circles or even 3 circles.
Where you say the surface area of the cone includes one circle, surface area of the cylinder involves 2 circles for a total of 3. But if you look at how we broke it down we only calculate the surface area of 1 circle. So that's going to be a trick when you're trying to solve problems where you have joined solids. Identify where they overlap and make sure you don't double count anything.
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