Fun with 3D Shapes: Volume Formulas and Pyramid Surface Areas!

Open

Chandrakshi

5/8/2023

Algebra 1

7th/8th Grade Geometry

Subjects

Algebra 1

Fun with 3D Shapes: Volume Formulas and Pyramid Surface Areas!

A comprehensive guide to volume formulas for 3D shapes and surface area calculations, covering various geometric solids including prisms, pyramids, cylinders, cones, and spheres.

Detailed exploration of 3D figures and their characteristics, including face counts and base types
In-depth coverage of surface area calculations with practical examples
Comprehensive formulas for volume calculations of different shapes
Special focus on calculating surface area of pyramids and identifying characteristics of cones
Advanced concepts including composite shapes and their volume calculations
Step-by-step problem-solving examples for real-world applications

5/8/2023

32
Name
Cylinder
3D Fgures & Nets
IDENTIFYING 3D FIGURES
3D Figure
#
Triangle Prim
Cube
Rectangular
Triangular
Prism
Rectangular
Pyramid
Tri

Page 2: Surface Area Calculations

This page focuses on surface area formulas and their applications for various geometric shapes. It provides detailed examples of calculating surface areas for different figures.

Definition: Surface area is the total area of all faces and bases of a 3D object.

Example: For a rectangle, the area is calculated using A = l × w (length times width).

Highlight: Surface area calculations require adding the areas of all faces and bases.

Vocabulary: Base refers to the bottom face of a 3D shape.

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Page 3: Volume of Prisms and Pyramids

This page covers volume calculations for prisms and pyramids, providing essential formulas and practical examples.

Definition: Volume is the amount of space occupied by a three-dimensional object.

Example: The volume of a rectangular prism is calculated by multiplying length × width × height.

Highlight: Pyramid volumes are always one-third of the volume of a prism with the same base and height.

View

Page 4: Volume of Cylinders

This page details cylinder volume calculations with practical applications and problem-solving examples.

Definition: The volume of a cylinder is calculated using the formula V = πr²h.

Example: A can of potato chips with height 28cm and volume 3165cm³ can be solved for its diameter.

Vocabulary: Radius (r) is half the diameter of a circle.

View

Page 5: Volume of Cones

This page explores cone volume calculations and their relationship to cylinders.

Highlight: A cone's volume is one-third of a cylinder with the same base and height.

Example: For a cone with volume 400cm³ and height 10cm, the radius can be calculated using V = πr²h/3.

Definition: The volume of a cone is calculated using V = πr²h/3.

View

Page 6: Volume of Spheres

This page covers sphere volume calculations with various practical examples.

Definition: The volume of a sphere is calculated using V = 4/3πr³.

Example: A beach ball with diameter 12 inches has a volume of 904.32 cubic inches.

Highlight: Sphere volumes depend only on the radius cubed.

View

Page 7: Composite Shapes

This page explains how to calculate volumes of composite shapes by breaking them down into basic geometric forms.

Definition: Composite shapes are formed by combining multiple basic 3D shapes.

Example: A shape combining a cylinder, sphere, and cone requires calculating each volume separately and then adding them together.

Highlight: Complex shapes can be broken down into simpler geometric forms for volume calculations.

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Subjects

Algebra 1

Fun with 3D Shapes: Volume Formulas and Pyramid Surface Areas!

Chandrakshi

@ch_10s

15 Followers

A comprehensive guide to volume formulas for 3D shapes and surface area calculations, covering various geometric solids including prisms, pyramids, cylinders, cones, and spheres.

Detailed exploration of 3D figures and their characteristics, including face counts and base types
In-depth coverage of surface area calculations with practical examples
Comprehensive formulas for volume calculations of different shapes
Special focus on calculating surface area of pyramids and identifying characteristics of cones
Advanced concepts including composite shapes and their volume calculations
Step-by-step problem-solving examples for real-world applications

...

5/8/2023

394

7th/8th

Algebra 1

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Page 2: Surface Area Calculations

This page focuses on surface area formulas and their applications for various geometric shapes. It provides detailed examples of calculating surface areas for different figures.

Definition: Surface area is the total area of all faces and bases of a 3D object.

Example: For a rectangle, the area is calculated using A = l × w (length times width).

Highlight: Surface area calculations require adding the areas of all faces and bases.

Vocabulary: Base refers to the bottom face of a 3D shape.

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Page 3: Volume of Prisms and Pyramids

This page covers volume calculations for prisms and pyramids, providing essential formulas and practical examples.

Definition: Volume is the amount of space occupied by a three-dimensional object.

Example: The volume of a rectangular prism is calculated by multiplying length × width × height.

Highlight: Pyramid volumes are always one-third of the volume of a prism with the same base and height.

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Page 4: Volume of Cylinders

This page details cylinder volume calculations with practical applications and problem-solving examples.

Definition: The volume of a cylinder is calculated using the formula V = πr²h.

Example: A can of potato chips with height 28cm and volume 3165cm³ can be solved for its diameter.

Vocabulary: Radius (r) is half the diameter of a circle.

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Page 5: Volume of Cones

This page explores cone volume calculations and their relationship to cylinders.

Highlight: A cone's volume is one-third of a cylinder with the same base and height.

Example: For a cone with volume 400cm³ and height 10cm, the radius can be calculated using V = πr²h/3.

Definition: The volume of a cone is calculated using V = πr²h/3.

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Page 6: Volume of Spheres

This page covers sphere volume calculations with various practical examples.

Definition: The volume of a sphere is calculated using V = 4/3πr³.

Example: A beach ball with diameter 12 inches has a volume of 904.32 cubic inches.

Highlight: Sphere volumes depend only on the radius cubed.

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Page 7: Composite Shapes

This page explains how to calculate volumes of composite shapes by breaking them down into basic geometric forms.

Definition: Composite shapes are formed by combining multiple basic 3D shapes.

Example: A shape combining a cylinder, sphere, and cone requires calculating each volume separately and then adding them together.

Highlight: Complex shapes can be broken down into simpler geometric forms for volume calculations.

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Page 1: 3D Figures and Their Characteristics

This page introduces fundamental concepts of three-dimensional figures and their nets. The content covers various 3D shapes including prisms, pyramids, cylinders, and cones, detailing their basic characteristics.

Definition: A 3D figure is a geometric shape that has length, width, and height.

Highlight: Each 3D shape has unique characteristics defined by the number of faces and base types.

Example: A cube has 6 faces and square bases, while a cylinder has 2 faces with circular bases.

Vocabulary: Nets are flat patterns that can be folded to create 3D shapes.

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Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

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4.9+

Average App Rating

17 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User