3-D shapes have length, width, and height. A cube has 6 faces, 12 edges, and 8 vertices. The surface area of a cube can be found by calculating the area of each face, which is the length squared, and multiplying by 6 since there are 6 faces. The surface area of other 3-D shapes like cuboids and cylinders can be found by calculating the total area of all faces, such as using the formula for a cuboid of 2 times the length times width plus 2 times the height times width plus 2 times the length times height. The surface area of a cylinder is 2 times pi times the radius times the height plus 2 times pi times the radius squared.

5. 3-D stands for three-dimensional.
3-D shapes have length, width and height.
For example, a cube has equal length, width and height.
How many faces does a cube
have?
6
How many edges does a cube
have?
12
Face
Edge
Vertex
How many vertices does a cube
have?
8

8. How can we find the surface area of a cube of length x?
All six faces of a cube have the same
area.
The area of each face is x × x = x2
Therefore,
x
Surface area of a cube = 6x2

10. To find the surface area of a shape, we calculate the total area of all
of the faces.
A cuboids has 6 faces.
The top and the bottom of the cuboids
have the same area.

11. To find the surface area of a shape, we calculate the total area of all
of the faces.
A cuboid has 6 faces.
The front and the back of the cuboid
have the same area.

12. We can find the formula for the surface area of a cuboid as follows.
Surface area of a cuboid =
l
w
2 × lw
h
Top and bottom
+ 2 × hw
Front and back
+ 2 × lh
Left and right side
= 2lw + 2hw + 2lh

13. To find the surface area of a shape, we calculate the total area of all
of the faces.
A cuboid has 6 faces.
The left hand side and the right hand
side of the cuboid have the same
area.

15. SURFACE AREA of a CYLINDER.
Imagine that you can
open up a cylinder like
so
You can see that
the surface is
made up of two
circles and a
rectangle.
The length of the rectangle is the same
as the circumference of the circle!

16. EXAMPLE: Round to the nearest TENTH.
Top or bottom circle
Rectangle
A = πr²
C = length
The length is the same as
the Circumference
A = π(3.1)²
A = π(9.61)
A = 30.2 cm²
C=πd
C = π(6.2)
C = 19.5 cm
Now the area
Now add:
30.2 + 30.2 + 234 =
SA = 294.4 in²
A = lw
A = 19.5(12)
A = 234 cm²

17. This could be written a different way.
2πr = πd
So this formula could be written:
SA = 2πr² + πd ·h
A = πr² (one circle)
This is the area of the top and
the bottom circles.

18. There is also a formula to find surface area of a cylinder.
Some people find this way easier:
SA = 2πrh + 2πr²
SA = 2π(3.1)(12) + 2π(3.1)²
SA = 2π (37.2) + 2π(9.61)
SA = π(74.4) + π(19.2)
SA = 233.7 + 60.4
SA = 294.1 in²
The answers are REALLY close, but not exactly the same. That’s because
we rounded in the problem.

20. 

A cone has a circular base and a vertex that is not in the
same plane as a base.
In a right cone, the height meets the base at its center.
The vertex is directly
above the center of
the circle.
Height
Lateral Surface
Slant Height
r
Base


r
The height of a cone is the perpendicular distance
between the vertex and the base.
The slant height of a cone is the distance between the
vertex and a point on the base edge.

21. 
Surface Area = area of base + area of sector
= area of base + π(radius of base)(slant height)
S  B   r    r   r
2

B r
2
r

23. 
The volume of a sphere with radius r
is S = 4r3.
3

24. The point is called the center of the
sphere. A radius of a sphere is a
segment from the center to a point
on the sphere.
 A chord of a sphere is a segment
whose endpoints are on the
sphere.


25. 
A diameter is a chord that contains
the center. As with all circles, the
terms radius and diameter also
represent distances, and the
diameter is twice the radius.

26. 
The surface area of a sphere with
radius r is S = 4r2.

27. AREA of a CIRCLE
C=2πr
1/2C=πr
Radius (r)
height (h) = r
1/2C=πr
A = base x height
A = πr x r
A=
2
πr
base (b)= πr