volume of pyramids and cones\nin this activity, youll define and apply relationships between the volumes of…
volume of pyramids and cones\nin this activity, youll define and apply relationships between the volumes of prisms, pyramids, and cones.\nquestion 1\nthe prism shown in the diagram has a volume of 39 units³.\nwhat is the volume of the pyramid? explain your reasoning.
Answer
Explanation:
Step1: Recall the volume relationship
The volume of a pyramid is one - third of the volume of a prism with the same base and height. The formula for the volume of a prism is (V_{prism}=Bh) (where (B) is the area of the base and (h) is the height), and the formula for the volume of a pyramid is (V_{pyramid}=\frac{1}{3}Bh). In this case, the prism and the pyramid have the same base (with length (a), width (b)) and the same height (c).
Step2: Calculate the volume of the pyramid
Given that the volume of the prism (V_{prism} = 39) units³. Using the relationship (V_{pyramid}=\frac{1}{3}V_{prism}), we substitute (V_{prism}=39) into the formula. So (V_{pyramid}=\frac{1}{3}\times39). Calculating (\frac{1}{3}\times39 = 13).
Answer:
The volume of the pyramid is 13 units³.