Given a rectangular pyramid and a rectangular prism that have the same base and same height, how do their volumes compare? If the pyramid was full of water, how much of the prism would it fill up? Name another pair of three-dimensional objects that have a relationship similar to this.
Accepted Solution
A:
we know that volume of a rectangular prism =B*h------> equation 1 where B is the area of the base h is the height
volume of a rectangular pyramid=(1/3)*B*h-----> equation 2 where B is the area of the base h is the height
substitute equation 1 in equation 2 volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
the answer part a) is volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
Part b) If the pyramid was full of water, how much of the prism would it fill up?
the answer part b) is If the pyramid was filled with water, the prism would only fill 1/3 of its volume
Part c) Name another pair of three-dimensional objects that have a relationship similar to this
cones and cylinders
volume of a cylinder =B*h------> equation 1 where B is the area of the base h is the height
volume of a cone=(1/3)*B*h-----> equation 2 where B is the area of the base h is the height
substitute equation 1 in equation 2 volume of a cone=(1/3)*volume of a cylinder