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Surface Area (Using Formulas)
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What you will learn from this videoWhat you will learn
- We'll learn how to find surface area using formulas.
- We'll also learn where these formulas come from.
- And we'll see how this knowledge can help us make a pizza box, start a slushy business, and even make a treehouse.
- Discussion Questions
Before Video
How do you find the area of a rectangle? Square? Circle?ANSWERArea of a rectangle is l x w. Area of a square is the same, but all the sides are the same, so I can just use s x s or s^{2}. Area of a circle is πr^{2}.
Area of a rectangle is l x w. If I draw a line from one corner of the rectangle to the opposite corner, I cut the rectangle in half and make two identical right triangles. Therefore, the area of a triangle is half of the area of a rectangle. For a triangle, I call the dimensions base and height instead of length and width. Area of a triangle is [ggfrac]b x h/2[/ggfrac].
Surface area is the total of the areas of the faces of a shape added together. If I wanted to cover a shape in paper, I would want to know the total surface area.
A rectangular prism has 6 faces, and each pair of opposite faces are the same. So there are up to 3 different faces. A triangular prism has 5 faces, and the two triangular faces are the same, so there are up to 4 different faces.
In the formula, I substitute 3 for b and 4 for h. Then the expression becomes A = [ggfrac]3 x 4/2[/ggfrac], which is equal to 6 cm^{2}. The answer is in square units for area.
After Video
The formula for the surface area of a cube is 6s^{2}. If a side of the cube measures 3 m, how can you find the surface area of the whole cube?ANSWERFirst calculate the power before multiplying by 6. 6s^{2} means 6 x s x s, and since s = 3, the expression becomes 6(3)^{2} or 6 x 3 x 3 = 48 m^{2}.
Yes! A cube is a type of rectangular prism. I can use the formula 2l×w+2w×h+2(l×h), but l, w, and h all have the same value, so the result is the same as using for formula 6s^{2}.
I need both! The formula for area of a circle gives the area of the circles at either end of the cylinder. The formula for the circumference of a circle gives the length of the rectangle formed by unrolling the cylinder.
The base of the triangle, b, is also the width of one of the rectangles. In this triangular prism, the height of the triangle, h, is the width of another rectangle, so it could also be labeled a. The third side of the triangle is labeled c, the width of the third rectangle. The dimension d is the height of the prism, and the length of all 3 rectangles.
Slant height is the measurement from the tip of the cone, along the side, down to where the side connects with the circular base. It is different from the actual height of the cone, which is measured at a right angle from the tip to the center of the base.
- Vocabulary
- Rectangular Prism DEFINE
A shape made of 6 rectangular faces. The opposite faces always have the same dimensions.
- Cube DEFINE
A rectangular prism whose sides all have the same length so that all 6 faces are squares.
- Face DEFINE
Each flat part of a shape that we can calculate an area for.
- Triangular Prism DEFINE
A shape that has 2 parallel triangular faces connected by 3 rectangular faces.
- Cylinder DEFINE
A shape that looks like a tube with a circular lid on each end.
- Cone DEFINE
A shape that has a circular base and a slanted edge that extends from around the base to meet at a point.
- Slant height DEFINE
In a 3D cone or pyramid, the slant height is the length from the edge of base to the point at the top. It is not the same as the actual height of the object.
- Rectangular Prism DEFINE
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