Mathematics

Question

A cylindrical 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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A cylindrical center has been removed from the triangular prism shown above. Which is closest to the volume of the remaining portion of the triangular prism? Us

1 Answer

  • 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 :)
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