Acylindrical center has been removed from the triangular prism shown above. which is closest to the volume of the remaining portion of the triangular prism? use 3.14 as an approximation for π.

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First we should figure out the volume of the prism (ignoring the cylinder at the moment)

(base * height/2)*depth
We need to find the height of the triangle which can be done with pythagoras because this is a right angled triangle (as shown by the little square at the bottom) 
12 is the hypotenuse.

√12²-10² =6.63 (rounded)
Now we have the height of the triangle and can find the volume.

12*6.63/2*15=596.7

Now we find the volume of the cylinder.
area of circle * depth

area=3.14*1.5²
3.14*2.25
7.065

7.065*15=105.975

Now we subtract the volume of the cylinder from the volume of the prism and you have:
596.7-105.975
490.725 which is your answer

Hope this helps :)