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INTRODUCTION*NAME-PIYUSH BHANDARI
*CLASS- 9*SUBJECT- MATHS POWER POINT PRESENTATION
*SECTION- A*SUBMITTED TO- GARIMA JAIN
SURFACE AREAS OF ALL THE 3D FIGURES
SOME EXAMPLE OF 3D FIGURES
*CUBE*CUBOID
*CYLINDER*CONE
*SPHEREAnd
*HEMISPHERE
3-D shapes
3-D stands for three-dimensional.
3-D shapes have length, width and height.
For example, a cube has equal length, width and height.
Face
Edge Vertex
How many faces does a cube have? 6
How many edges does a cube have? 12
How many vertices does a cube have? 8
1. CUBE
To find the Surface areas of 3D cube
How can we find the surface area of a cube of length x?
Surface area of a cube
x
All six faces of a cube have the same area.
The area of each face is x × x = x2
Therefore,
Surface area of a cube = 6x2
2. CUBOID
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.
Surface area of a cuboids
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.
Surface area of a cuboids
We can find the formula for the surface area of a cuboid as follows.
Surface area of a cuboid =
Formula for the surface area of a cuboids
h
lw
2 × lw Top and bottom
+ 2 × hw Front and back
+ 2 × lh Left and right side
= 2lw + 2hw + 2lh
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.
Surface area of a cuboids
3.CYLINDER
SURFACE AREA of a CYLINDER.
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!
Imagine that you can open up a cylinder like so
EXAMPLE: Round to the nearest TENTH.
Top or bottom circle
A = πr²
A = π(3.1)²
A = π(9.61)
A = 30.2 cm²
Rectangle
C = length The length is the same as the Circumference
C = π dC = π(6.2)C = 19.5 cm
Now the area
A = lwA = 19.5(12)A = 234 cm²
Now add:
30.2 + 30.2 + 234 =
SA = 294.4 in²
This could be written a different way.
A = πr² (one circle)This is the area of the top and the bottom circles.2πr = πd
So this formula could be written:
SA = 2πr² + πd ·h
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)²SA = 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.
4.CONE
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 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.
Height
Lateral Surface
The vertex is directly above the center of the circle.
Baser
Slant Height
r
Surface Area of a Cone Surface Area = area of base + area of sector
= area of base + π(radius of base)(slant height)
S B r 2r r
2B r r
5.SPHERE
Theorem 12.12: Volume of a Sphere
The volume of a sphere with radius r is S = 4r3.
3
Finding the Surface Area of a Sphere
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.
Finding the Surface Area of a Sphere
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.
Theorem 12.11: Surface Area of a Sphere
The surface area of a sphere with radius r is S = 4r2.
AREA of a CIRCLE
Radius (r)
C=2πr
1/2C=πr
1/2C=πr
base (b)= πr
height (h) = r
A = base x height
A =
A = πr2x rπr