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.

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

For this you would want to break this figure up with familar shapes. You can do two triangles and one big rectangle.

First triangle:

(3)(2)(1/2)= 3 feet squared

Second Triangle:

(3)(4)(1/2)= 6 feet squared

Rectangle:

(11)(3)= 33 feet squared

Now you add:

33+3+6= 42 feet squared

So, for this hole you will need 42 feet squared of outdoor carpet