E. Surface Area of Right Prisms and Right Cylinders
E. Surface Area of Right Prisms and Right Cylinders
Recall that a right prism is a prism where the surfaces of the bases are parallel to each other and aligned with one directly above the other. The sides of these prisms are all rectangles.
The bases (shaded) are aligned with each other and the sides (non-shaded) are all rectangles.
Non-Right Prisms:
The bases (shaded) are not aligned with each other and the sides (non-shaded) are not all rectangles.
Similarly, a right cylinder is a cylinder where the circular bases are parallel and aligned directly with each other.
To find the surface area of a three-dimensional object, the two-dimensional shapes that make up the surfaces of the object must first be defined.
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Surface area
The surface area of a three-dimensional object is the total area of the object's net. |
The following are surface area formulas of familiar three-dimensional objects.
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Right Rectangular Prism
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Right Triangular Prism
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Right Cylinder
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| For all calculations: When «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«/math» is used in a formula, use the «math style=¨font-family:`Times New Roman`¨ xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«/math» function of your calculator. |
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Example 1 |
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A right cylinder is given with a radius of 2.5 cm and a height of 7.5 cm. Determine the surface area of the cylinder, to the nearest tenth of a square centimetre. Step 1: Identify the known values.
Step 2: Choose the appropriate surface area formula and substitute the known values into the formula.
Step 3: Compute the surface area.
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is the symbol for approximately equal to.
Note that when a right triangle is used as the base for a right triangular prism, the formula can be simplified:
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This is because the height of the triangle in this case also functions as one of the side-lengths of the triangle.