Surface Area & Volume
Calculate surface area and volume of 3D shapes
lessons (10)
Introduction to Surface Area
Learn what surface area is and how to calculate the total area covering a 3D shape.
Surface Area of Rectangular Prisms
Learn how to calculate the total surface area of rectangular prisms using a simple formula.
Surface Area of Cubes
Learn how to calculate the total surface area of a cube using the formula SA = 6s².
Surface Area of Cylinders
Learn how to calculate the total surface area of a cylinder using radius and height.
Surface Area of Cones
Learn to calculate the total surface area of cones using the radius, height, and slant height.
Surface Area of Spheres
Learn to calculate the surface area of a sphere using the formula SA = 4πr².
Surface Area of Pyramids
Learn how to calculate the total surface area of pyramids by combining the base area with the lateral face areas.
Volume vs Surface Area
Learn to distinguish between volume and surface area, understand when to use each, and solve real-world problems involving both concepts.
Surface Area of Composite Shapes
Learn to calculate the surface area of complex 3D shapes made by combining or subtracting basic solids.
Surface Area Word Problems
Learn to solve real-world problems involving surface area calculations for various 3D shapes.
Surface area measures the total area covering a 3D object, while volume measures the space inside. These concepts apply to real situations from calculating paint needed for walls to determining tank capacity. Understanding the relationship between dimensions and these measurements reveals how small changes dramatically affect quantities.
What Students Will Learn
- Calculate surface area of prisms and cylinders
- Calculate volume of prisms, cylinders, and cones
- Apply formulas for spheres
- Solve composite solid problems
- Understand how scaling affects surface area and volume
Frequently Asked Questions
How does doubling dimensions affect volume?
Doubling all dimensions multiplies volume by 8 (2³). Volume scales with the cube of the linear scale factor.
Why is surface area squared but volume cubed?
Surface area is 2-dimensional (length × width), measured in square units. Volume is 3-dimensional (length × width × height), measured in cubic units.
What is the volume of a sphere?
$V = \frac{4}{3}\pi r^3$. The surface area is $A = 4\pi r^2$.