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A rectangular prism has a volume of 252 in. ^(3). If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid? (1 point)

A rectangular prism has a volume of 252252 in. 3 { }^{3} . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid? (11 point)

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Full solution

Q. A rectangular prism has a volume of 252252 in. 3 { }^{3} . If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid? (11 point)
  1. Understand Relationship: Understand the relationship between the volume of a prism and a pyramid. The volume of a pyramid is 13\frac{1}{3} the volume of a prism with the same base area and height.
  2. Calculate Volume: Calculate the volume of the pyramid using the volume of the prism.\newlineSince the volume of the prism is 252 in.3252 \text{ in.}^3, the volume of the pyramid will be one-third of this.\newlineVolume of pyramid = (1/3)×(1/3) \times Volume of prism\newlineVolume of pyramid = (1/3)×252 in.3(1/3) \times 252 \text{ in.}^3
  3. Perform Calculation: Perform the calculation to find the volume of the pyramid.\newlineVolume of pyramid = (13)×252(\frac{1}{3}) \times 252\newlineVolume of pyramid = 84 in.384 \text{ in.}^{3}

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