The shape in the figure is to be submerged in water. How much water, in cubic centimeters, would be displaced by the prism?
We are asked to give our answer in cubic centimeters. This means that the amount of water that will be displaced is equal to the volume of the prism. The volume of any prism can be calculated by multiplying the area of the cross section by its length. In this question, the cross section is a triangle. We can calculate the area of any triangle by multiplying the base by the perpendicular height and then dividing by two.
As all of our units are in centimeters, in this question, this is multiplying six by five and then dividing by two. The length of the prism is 15 centimeters. So, we need to multiply this answer by 15. Six multiplied by five is equal to 30. Dividing this by two or halving it gives us 15. Multiplying 15 by 15 gives us 225.
The volume of the triangular prism is 225 cubic centimeters, which means that this is the amount of water that is displaced.