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Volume of Triangular Pyramids Assessment

Questions
Age 13–14
English

Volume of Triangular Pyramids Assessment

Part 1: Multiple Choice Questions

  1. A triangular pyramid has a base area of
    
    and a height of
    
    . What is its volume? A)
    
    B)
    
    C)
    
    D)
    
  1. Find the volume of a triangular pyramid with a base triangle having a base of
    
    and an altitude of
    
    , and a pyramid height of
    
    . A)
    
    B)
    
    C)
    
    D)
    
  1. The volume of a triangular pyramid is
    
    . If the area of the base is
    
    , what is the height of the pyramid? A)
    
    B)
    
    C)
    
    D)
    
  1. Which of the following is the correct formula for the volume of any pyramid, including a triangular one? A)
    
    B)
    
    C)
    
    D)
    
  1. A crystal paperweight in the shape of a triangular pyramid has a volume of
    
    and a height of
    
    . What is the area of its base? A)
    
    B)
    
    C)
    
    D)
    


Part 2: Open-ended Prompts

  1. Look at the diagram below and calculate the volume of the triangular pyramid. Show your steps.
Figure 1: A triangular pyramid with base dimensions and height labeled.
Figure 1: A triangular pyramid with base dimensions and height labeled.

  1. A triangular pyramid has a base that is a right-angled triangle with sides
    
    ,
    
    , and
    
    . If the height of the pyramid is
    
    , find its volume.
  1. If you double the height of a triangular pyramid but keep the base area the same, how does the volume change? Explain your answer using the formula.
  1. A pyramid and a prism have the same base area and the same height. If the volume of the prism is
    
    , what is the volume of the triangular pyramid? Show your calculation.
  1. A triangular pyramid has a volume of
    
    . The base triangle has an altitude of
    
    and the pyramid has a height of
    
    . What is the length of the base of the triangle?