Cement was poured to make two rectangular prism the prism were stacked as shown 4 feet 3 feet 4 feet 3 feet 2 feet what are lengths , width, height in feet of the smaller rectangular prism

V_t = 72 ft^3

Step-by-step explanation:

Solution:-

- The complete question is given in the attachment.

a)

- The length of the smaller rectangular prism ( l ) is the side that runs along horizontal to the page and marked by l = 4 feet.

- The width of the smaller rectangular prism ( w ) is the side that protrudes out of the page, and also share the same dimension as the larger rectangular prism and marked by w = 2 feet.

- The height of the smaller rectangular prism ( h ) is the side that runs vertical to the page and marked by h = 3 feet.

- So the dimensions of the smaller rectangular prism are:

                  ( l , w , h ) = ( 4 , 2 , 3 ) feet

- Similarly, for the larger rectangular prism:

- The length of the larger rectangular prism ( L ) is the side that runs along horizontal to the page and the sum of smaller and upper exposed face length, totaling to L = ( 4 + 4 )  = 8 feet.

- The width of the larger rectangular prism ( W ) is the side that protrudes out of the page, and also share the same dimension as the larger rectangular prism and marked by W = 2 feet.

- The height of the larger rectangular prism ( h ) is the side that runs vertical to the page and marked by H = 3 feet.

- So the dimensions of the larger rectangular prism are:

                  ( L , W , H ) = ( 8 , 2 , 3 ) feet

b)

- The total amount of cement in cubic feet required to make two rectangular prism with dimensions evaluated above is the sum of smaller and larger rectangular prism volumes.

- The volume of a rectangular prism is given by:

                  V-prism = Length*width*height

- So the total volume V_t would be:

                  V_t = V_small + V _large

                  V_t = ( l*w*h ) + ( L*W*H )

                  V_t = ( 4*2*3 ) + ( 8*2*3 )

                  V_t = ( 4*2*3 ) + ( 8*2*3 )

                  V_t = ( 24 ) + ( 48 )

                  V_t = 72 ft^3