Key Concepts:
- NOTE: All volume formulas below will be given to you as references in the real test.
- Volume of Rectangular Prism: (V = lwh).
- Volume of a Cube: (V = s^3).
- Volume of a Cylinder: (V = \pi r^2 h).
- Volume of a Sphere: (V = \frac{4}{3} \pi r^3).
- Volume of a Cone: (V = \frac{1}{3} \pi r^2 h).
- Volume of a Pyramid: (V = \frac{1}{3} lwh).
- Surface Area of 3D Shapes:
- Rectangular Prism: (SA = 2(lw + lh + wh)).
- Cube: (SA = 6s^2).
- Cylinder: (SA = 2\pi r(h + r)).
Skills Covered:
- Calculating the height of a prism/cylinder given its volume and base area.
- Determining the volume of a 3D shape with necessary parameters given.
- Finding the surface area of a cube/sphere when given its volume.
- Calculating the surface area of a 3D shape.
- Extracting cube roots when given the volume of a cube.
Example Problems:
- A prism has a base of 18 square units and a height of 10 units. What is the volume, in cubic units, of the prism?
- A cube has a volume of 27. What is its surface area?
- What is the volume and surface area of a cylinder with a 2-centimeter radius and a 5-centimeter height?