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