Common Core: 8th Grade Math

Explore the foundational concepts of mathematics, including algebra, geometry, and data analysis, essential for 8th-grade students.

Linear Equations and FunctionsThe Pythagorean TheoremData Analysis and Statistics
Systems of Linear EquationsVolume of Cylinders, Cones, and SpheresTransformations and Congruence
Budgeting and Money MathMath in Sports and GamesEngineering and Design
Breaking Down Word ProblemsChecking Your Work
Linear Equations and...The Pythagorean Theo...Data Analysis and St...Systems of Linear Eq...Volume of Cylinders,...Transformations and ...Budgeting and Money ...Math in Sports and G...Engineering and Desi...Breaking Down Word P...Checking Your Work
Advanced Topics

Volume of Cylinders, Cones, and Spheres

Measuring 3D Shapes

In 8th grade, we move beyond flat shapes and measure how much space is inside 3D shapes like cylinders, cones, and spheres.

Formulas to Remember

  • Cylinder: \( V = \pi r^2 h \)
  • Cone: \( V = \frac{1}{3} \pi r^2 h \)
  • Sphere: \( V = \frac{4}{3} \pi r^3 \)

Here, \( r \) is the radius, \( h \) is the height, and \( \pi \) (pi) is about 3.14.

Real-Life Uses

Knowing the volume helps us figure out how much fits inside containers, how much water a tank can hold, or how much air is in a ball.

Examples

  • A water tank shaped like a cylinder with radius 2 meters and height 5 meters holds \( \pi \times 2^2 \times 5 = 62.8 \) cubic meters.

  • A scoop of ice cream is a sphere with radius 3 cm. Its volume is \( \frac{4}{3} \pi \times 3^3 \approx 113 \) cubic centimeters.

In a Nutshell

Finding the volume of 3D shapes helps us measure and compare how much they can hold.

Key Terms

Volume
The amount of space inside a 3D object.
Cylinder
A 3D shape with two parallel circular bases connected by a curved surface.
Cone
A 3D shape with a circular base that narrows to a point.
Sphere
A perfectly round 3D shape, like a ball.
Next
Transformations and Congruence