3D Shapes Game

Volume of 3D Shapes

Volume of 3D Shapes on Prezi

Cylinder

cylinder

                                                

A cylinder is actually  two circles (one on the top and one on the bottom) and a rectangle in the middle.  The base is the same as the top and also between. It has one curved side. If we cut the middle  and lay it flat, it would  form a rectangle. The circumference  of the circle actually  forms the base of  the rectangle. Because it has a curved surface, it is not a polyhedron.

To calculate the VOLUME  of a CYLINDER, use this formula: V = πr2h

Just multiply the area of the circle by the height of the cylinder:

• Area of the circle: π × r²
• Height: h
• Volume = Area × Height = π × r² × h

Volume of a Cone vs Cylinder

The volume formulas for cones and cylinders are very similar:

The volume of a cylinder is:	π × r2 × h
The volume of a cone is:	π × r2 × (h/3)

So, the only difference is that a cone's volume is one third (¹/₃) of a cylinder's.

So, in future, order your ice creams in cylinders, not cones, you get 3 times more!

Pyramid

pyramid

Square Pyramid Fact When we think of pyramids we think of the Great Pyramids of Egypt. They are actually Square Pyramids, because their base is a Square. It has 5 faces. The 4 side faces are triangles. The base is square. It has 5 vertices (corner points). It has 8 edges. When all side faces are the same: Surface area = Base area + 1/2 x perimeter x (slant length) When side faces are different:  [Base Area] + [Lateral Area] Volume = 1/3 x (base area) x height

Cube

       

cube 

The cube has 6 sides, 8 vertices, and 12 edges To find the surface area of a cube,   find the area of one side (L x W), and then multiply by the total number of  sides (6).  Remember to count all the hidden sides!  If all three lengths are equal it can be called a cube (or hexahedron) and each face will be a square. A cube is still a prism. And a cube is one of the Platonic Solids.

 SURFACE AREA = (L x W) x 6 

Volume is the amount of space a three-dimensional shape occupies.  To find the volume of a shape, use this formula: Length x Width x Height.

VOLUME = L x W x H

Cuboid

cuboid

Cuboid is a polyhedron with six rectangular plane faces. There are 12 edges and 8 vertices in a cuboid. Cuboid is also called as right rectangular prism or rectangular parallelepiped box.  If all the edges of a cuboid are equal then it forms a cube. In a cuboid opposite faces are equal and parallel and all angles are right angles. Cuboids are the simplest of all solid shapes, with six faces consisting of squares and rectangles.Cuboids are very common in our world, from boxes to buildings we see them everywhere. You can even fit them inside other cuboids!

A = 2wl + 2lh + 2hw

V = 4×5×10 = 200 A = 2×4×5 + 2×5×10 + 2×10×4    = 40+100+80 = 220

The cuboid has 6 sides, 8 vertices, and 12 faces.  To calculate the surface area or volume of the cuboid, use the same formula as you would for the cube.

Note: The name "cuboid" comes from "cube" and -oid (which means "similar to, or resembling") and so indicates "it is like a cube".
Another use of -oid is when we talk about the Earth being a spheroid (not exactly a sphere, but close).

Sphere

A sphere is a set of points in three dimensional space equidistant from a point called the center of the sphere. The distance from the center to the points on the sphere is called the radius of the sphere. Notice that we are talking about the surface of a ball, and not the ball itself. The surface of the earth we live on is a good approximation to a sphere. As you read through this material it would be helpful to have a beach ball about 12'' in diameter with a smooth, solid colored surface, a marking pen, preferably the kind that easily washes off, string, scissors, and a protractor. All points on the surface are the same distance from  the centre. It has no edges or vertices (corners).

Volume   = (4/3) × π ×r

Surface Area = 4× π × r²³

Cone

The flat face of a cylinder is circular. The cone has a curved face, a circular flat face and a vertex. The pointy end of a cone is called the vertex. The flat part is the base. An object shaped like a cone is said to be conical. Because it has a curved surface, it is not a polyhedron.

Surface area of base =π × r²

Surface area of side = π × r × s    or    π × r × √(r2+h2)

Volume =  π × r2 × (h/3)

Introduction to 3D Shapes

                    We live in a three-dimensional world. Every object you can see or touch has three dimensions that can be measured: length, width, and height. The room you are sitting in can be described by these three dimensions. The monitor you're looking at has these three dimensions. Even you can be described by these three dimensions. In fact, the clothes you are wearing were made specifically for a person with your dimensions.

                   In the world around us, there are many three-dimensional geometric shapes. In these lessons, you'll learn about some of them. You'll learn some of the terminology used to describe them, how to calculate their surface area and volume, as well as a lot about their mathematical properties.

• Faces refers to the sides of a shape.  
• A vertex is where two or more points meet; a corner. 
• The edge of a shape is the line where two surfaces meet.

REMEMBER:

 In a three-dimensional shape, you may not always be able to see all of the faces (sides)
 of the shape.