math q4

• Pyramid


  Solid figure with a polygonal base and triangular sides that meet at a common vertex
• Rectangular prism and pyramid with same base and height


  Volume of pyramid is 1/3 the volume of the rectangular prism
• Cylinder


  Solid figure with circular bases and curved sides
• Cone


  Solid figure with a circular base and curved sides that meet at a common vertex
• Cylinder and cone with same base and height


  Volume of cone is 1/3 the volume of the cylinder
• Sphere


  Solid figure that is perfectly round, with all points on the surface equidistant from the center
• Cylinder and sphere with same radius


  Volume of sphere is 4/3 the volume of the cylinder
• Volume of a rectangular prism = length x width x height
• Volume of a pyramid = 1/3 x base area x height
• Volume of a cylinder = π x radius^2 x height
• Volume of a cone = 1/3 x π x radius^2 x height
• Volume of a sphere = 4/3 x π x radius^3
• Volume


  The amount of space a solid figure occupies, measured in cubic units
• Finding the volume of a cone

  V = 1/3 (πr^2h)
• Volume of a cylinder


  Volume of a cone with the same dimensions is 1/3 the volume of the cylinder
• Volume of a cylinder


  Volume of a sphere with the same radius is 2/3 the volume of the cylinder
• Volume of a rectangular prism


  Volume of a pyramid with the same base and height is 1/3 the volume of rectangular prism
• Volume of a cylinder


  Volume of a prism with the same base and height as cone is the same
• Cylinder


  Solid figure with two circular bases that are congruent and parallel
• Pyramid

  Solid figure with one base, the other faces are triangles
• Cone


  Solid figure with one circular base and a vertex
• Sphere


  Set of all points in space that are the same distance from a given point called the center
• Finding the volume of a rectangular pyramid


  Multiply the area of the base by the height and divide by 3
• Finding the volume of a cylinder

  Multiply the area of the circular base by the height
• Finding the volume of a cone


  Multiply 1/3 by the area of the circular base and the height
• Finding the volume of a sphere


  Multiply 4/3 by π and the radius cubed
• Cube


  Solid figure with 6 square faces
• Cylinder

  Solid figure with 2 circular bases and a curved surface connecting them
• Solving routine and non-routine problems involving volumes of solids


  1. Understand the problem

  2. Plan a solution

  3. Carry out the plan

  4. Check the answer
• Four-step problem solving plan


  • Understand
  • Plan
  • Carry out
  • Check
• Volume of a cube

  Edge length x Edge length x Edge length
• Volume of a cylinder

  
  

  (π)(r^2)(h)
• Solving the problem

  1. Step 1: Understand

  2. Step 2: Plan

  3. Step 3: Solve

  4. Step 4: Check
• Volume of a cube

  V = e^3
• Volume of a cylinder

  V = πr^2h
• Volume of a hemisphere

  V = (2/3)πr^3