Surface Area of Surface Area of 3-Dimensional Figures3-Dimensional FiguresSurface Area of Surface Area of 3-Dimensional Figures3-Dimensional Figures

Ms. Stewart Ms. Stewart

Math 8Math 8

Outcome:D7: Estimate and calculate volumes and surface areas of right prisms and cylinders

COPY SLIDES WHEN YOU SEE THIS ICON

Many jobs in the real-world deal with using three-dimensional figures on two-dimensional surfaces. A good example of this is architects use drawings to show what the exteriors of buildings will look like.

Three-dimensional figures have faces, edges, and vertices.

A face - is a flat surfaceAn edge - is where two faces meetA vertex - is where three or more edges meet.

How many faces do most three-dimensional figures have?

With your isometric dot paper, sketch the drawing below. Make your box 3 units wide, 2 units high, and 5 units long.

Now try to sketch the box.

After you have sketched the box, try other figures like a cube or pyramid.

Drawing three-dimensional figures uses a technique called perspective. Here you make a two-dimensional figure look like it is three-dimensional.

Surface area of objects are used to advertise, inform, create art, and many other things. On the left is an anamorphic image, which is a distorted picture that becomes recognizable when reflected onto a cylindrical mirror.

One of the most recognizable forms of advertising that uses surface area of an object is the cereal box.Why would manufacturers want to know how much surface area a cereal box has?

If you find the surface area of the box you determine how much advertising space, space for promotions, nutrition information, how much cardboard is needed to make the box.

When you flatten-out a three-dimensional object the diagram is called a net.

Which of the following answers is the correct net for the cube. Choose a, b, c, or d.

Finding surface area of figures, for example the box below, can be relatively simple. All is needed is to visualize the faces and then use the appropriate area formulas for rectangles and circles.

Surface area is the sum of areas of all surfaces of a figure. The figure to the left is a rectangular prism. Notice how many surfaces there are. Lateral surfaces of a prism are rectangles that connect the bases.

Top and bottomLeft and rightFront and back

Lateral surfaces - of a cylinder is the curved surface.

How do I find the area of the lateral face of a cylinder?

How is the width in blue on the cylinder related to the width in blue of the rectangle?

How is the length (in red) of the rectangle related to the original cylinder?

What formula could you use to find the length of the rectangle, if you knew the radius of the cylinder?

c 2 r

The lateral surfaces of a triangular prism are triangles and rectangles.

Two triangular bases and three rectangles.

We express surface area in units squared (Ex. m2)

Finding Surface AreasFinding Surface AreasFinding Surface AreasFinding Surface Areas

Practice QuestionsPractice Questions

Find the surface area of the figure

SA = (top & bottom) + ( front & back) + (left & right)

= 2(8 · 6) + 2(8 · 2) + 2(6 · 2)= 96 + 32 + 24SA = 152 cm2

Find the surface area of the figure

SA = 2(πr2) + lw= 2(area of circle) + (circumference · height)= 2(3.14 · 3.12) + (π6.2) · 12= 60.3508 + 233.616= 293.9668 in2

Find the surface area of the figure

SA = 2(area of triangle) + (lw) + (lw) + (lw)= 2(½ · 12 · 16) + (20 · 12) + (16 · 12) + (12 · 12)= 192 + 240 + 192 + 144= 768 in2