Volume and surface area
This Grade 6 algebra skill from Yoshiwara Elementary Algebra covers volume and surface area of common three-dimensional figures. Students learn to calculate the volume (space inside) and surface area (total exposed surface) of prisms, cylinders, and other 3D shapes using standard formulas.
Key Concepts
Property • Volume is the amount of space contained within a three dimensional object. It is measured in cubic units, such as cubic feet or cubic centimeters.
• Surface area is the sum of the areas of all the faces or surfaces that contain a solid. It is measured in square units.
Common Formulas: Sphere: $V = \frac{4}{3}\pi r^3$, $S = 4\pi r^2$.
Common Questions
What is the difference between volume and surface area?
Volume measures the space inside a 3D shape (cubic units), while surface area measures the total area of all the outer surfaces of the shape (square units).
How do you calculate the volume of a rectangular prism?
Volume = length x width x height. For example, a box 3 cm by 4 cm by 5 cm has volume = 3 x 4 x 5 = 60 cubic centimeters.
How do you calculate the surface area of a rectangular prism?
SA = 2(lw + lh + wh), adding the areas of all 6 faces. For example, a 3 x 4 x 5 box has SA = 2(12 + 15 + 20) = 94 square centimeters.
What is the formula for the volume of a cylinder?
Volume = pi x r^2 x h, where r is the radius of the base and h is the height.
Where are volume and surface area taught in Grade 6?
Volume and surface area are covered in the Yoshiwara Elementary Algebra textbook for Grade 6.