 # Find Surface Area of Solids

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In this lesson, we will learn

• how to find the surface area of a cone
• how to find the surface area of a sphere
• how to find the surface area of joined solids
Surface Area of a Cone
Surface area is a two-dimensional property of a three-dimensional figure. Cones are similar to pyramids, except they have a circular base instead of a polygonal base. Therefore, the surface area of a cone is equal to the sum of the circular base area and the lateral surface area, calculated by multiplying half of the circumference by the slant height. Related topics include pyramid and cylinder surface area.
How to Find the Surface Area of a Cone. How to calculate the surface area of a cone when the slant height is not given?
The Pythagorean Theorem will be used to calculate the slant height using the radius and height of the cone as the right triangle's legs. Surface Area of a Sphere
In general, surface area is the sum of all the shapes that cover the surface of an object. To calculate the surface area of a sphere we multiply 4 by pi by the radius of the sphere squared. Given this formula, we can find the surface area of a sphere when given the radius. Similarly, we can find the radius of a sphere is we are given the surface area. This formula is very similar to other prism volume formulas.
Surface Area of a Sphere.
This video gives an example of finding the surface area of a sphere.

Review how to find the surface area of a sphere using the formula SA = 4(pi)(r)2
Surface Area of Joined Solids
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.
Composite Solid Surface Area

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