Evaluate without using a calculator by using ratios in a reference triangle sec 3pi/4
1 answer:
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Answer:
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
