Mr. Hill's Math
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  • Math 8
    • Number Sense >
      • 8.NS.1 - Rational and Irrational Numbers
      • 8.NS.2 - Estimating Irrational Numbers
    • Equation and Expressions >
      • 8.EE.1 & 8.EE.2 - Exponents
      • 8.EE.3 & 8.EE.4 - Scientific Notation
      • 8.EE.5 Graph and Compare Proportional Relationships
      • 8.EE.6 Similar Triangles and Relationships
      • 8.EE.7 - Solving Equations
      • 8.EE.8 Systems of Linear Equations
    • Functions >
      • 8.F.1 Inputs and Outputs & Function Machines
      • 8.F.2 Comparing Functions
      • 8.F.3 Types of Functions
      • 8.F.4 Constructing Functions
      • 8.F.5 Analyze and Graph Functions
    • Geometry >
      • 8.G.1 Geometric Transformations
      • 8.G.2 Congruent Shapes
      • 8.G.3 Effects of Transformations
      • 8.G.4 Similar Figures & Transformations
      • 8.G.5 Angle Relationships
      • 8.G.6, 8.G.7 & 8.G.8 The Pythagorean Theorem
      • 8.G.9 Volume of Cones, Cylinders * Spheres
    • Statistics and Probability >
      • 8.SP.1 Scatter Plot Trends
      • 8.SP.2 Best-fit Lines
      • 8.SP.3 Scatterplots and Equations
      • 8.SP.4 Two-way Tables
  • Math 7
    • Number Sense >
      • 7.NS.1 - Add and Subtract Rational Numbers
      • 7.NS.2 - Multiply and Divide Rational Numbers
      • 7.NS.3 - Solving problems with Rational Numbers
    • Equations and Expressions >
      • 7.EE.1, 7.EE.2 - Equivalent Linear Expressions >
        • 7.EE.1 - Expanding Linear Expressions
        • 7.EE.2 - Rewriting Linear Expressions
      • 7.EE.3, 7.EE.4 - Using Expressions to solve problems >
        • 7.EE.3 - Solving real-life problems
        • 7.EE.4 - Problem solving using simple variable equations
    • Ratios and Proportions >
      • 7.RP.1 - Unit rates with fractions
      • 7.RP.2 - Proportional Rates
      • 7.RP.3 - Multi-step Proportional Relationships
    • Statistics and Probability >
      • 7.SP.1, 7.SP.2 - Random Sampling and Inferences >
        • 7.SP.1 - Examining a Sample
        • 7.SP.2 - Inferences about a population
      • 7.SP.3, 7.SP.4 - Two Populations >
        • 7.SP.3 - Overlap of Data
        • 7.SP.4 - Comparative Inferences
      • 7.SP.5, 7.SP.6, 7.SP.7, 7.SP.8 - Probability >
        • 7.SP.5 - Understanding Probability
        • 7.SP.6 - Approximating Probability
        • 7.SP.7 - Probability Models
        • 7.SP.8 - Compound Probabilities
    • Geometry >
      • 7.G.1, 7.G.2, 7.G.3 - Geometric Figures >
        • 7.G.1 - Scale Drawings
        • 7.G.2 - Drawing Geometric Shapes
        • 7.G.3 - Cross Sections of Shapes
      • 7.G.4, 7.G.5, 7.G.6 - Calculating with Geometry >
        • 7.G.4 - Geometry of Circles
        • 7.G.5 - Unknown Angles
        • 7.G.6 - Real World Geometry
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8.G.9 - Volume and 3D Shapes - Solve real-world and mathematical problems involving volume of cylinders, cones and spheres. Know the formulas for the volumes of cones, cylinders and spheres and use them to solve real-world and mathematical problems.
Cylinders
As you see in the video to the right, to find the volume you need to know the radius and the height. Finding the volume is very similar to finding the area of a circle - you just multiply the area of a circle by the height.

First, find the area of the circle (π r^2). Then multiply it by the height. Finally, include your units in your answer.
Tips & Tricks
-Remember you need the radius, not the diameter

-You can use 3.14 for pi

-Your units would be cubed

- Think "No point at the top, no divide"

Cones
When finding the volume of a cone, you should be able to see this relates to a cylinder. Once you have the volume of a cylinder, you just divide by 3 to get the volume of the cone.


First, find the area of the base (π r^2). Then multiply by the height. Finally, divide by 3 to get the volume of the cone. Remember your units!
Tips & Tricks
- Remember to use the radius, not the diameter

- You can use 3.14 for pi

- Your units are cubed

- Think "Points at the top, so I have to divide by 3."

Spheres
For a sphere, the formula makes you take r and cube it, not square it. This is a big change compared to the two that you see above, the cylinder and the cone.


First, find the radius and cube it. Then multiply by 4 and then by pi. Finally, just divide it by 3.
- Remember to use the radius, not the diameter

- You can use 3.14 for pi

- Even though the shape is round, your units are still cubed

- Use 4/3 rather than 1.333. It is more accurate
Online Practice Problems
For each of the shapes in this standard, you can click on the image below and you will be taken to a website where you can see how the volume is computed. By simply sliding different points on the shapes, you can change the height or radius, and it will show you the volume of the shape. 
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