Answer:
Option D, the volume is 15.625 cubes
Step-by-step explanation:
For a cube of side length L, the volume is:
V = L^3
for the smaller cubes, we know that each one has a side length of 1 in, then the volume of each small cube is:
v = (1in)^3 = 1 in^3
Then:
1 in^3 is equivalent to one small cube
Here we know that the side length of our cube is (2 + 1/2) in
Then the volume of this cube will be:
V = [ (2 + 1/2) in]^3
To simplify the calculation, we can write:
2 + 1/2 = 4/2 + 1/2 = 5/2
Then:
V = ( 5/2 in)^3 = (5^3)/(2^3) in^3 = 125/8 in^3 = 15.626 in^3
This means that 15.625 small cubes will fill the prism.
So the correct option is D.
Option C: There are no solutions
Explanation:
The linear equations is graphed.
We need to determine the solution of the system of equations.
The solution of the equations can be determined by finding the point of intersection of the two equations.
From the figure, it is obvious that the two equations are parallel to each other.
Also, the parallel lines have the same slope and the parallel lines never intersect.
Hence, the system consisting of parallel lines have no solution.
Therefore, the solution to the system of linear equations graphed is no solution.
Thus, Option C is the correct answer.
14.6428 in decimal , in fraction 14 16/25
