Video: Finding the Height of a Prism given Its Volume and Its Base Area

A prism has volume 218.12 cubic meters and a base with area 13.3 square meters. Write an equation that can be used to find the height ℎ, then find the height of this prism.

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Video Transcript

A prism has volume 218.12 cubic metres and a base with area 13.3 square metres. Write an equation that can be used to find the height ℎ. Then, find the height of this prism.

So in this question, we’re being asked to do two things with the information we’ve been given. First, we’re asked to write an equation that can be used to find the height ℎ. And then, we’re being asked to solve our equation in order to actually find the height.

Let’s recall first of all then how we find the volume of a prism. We find the area of that prism’s base. It could be a square, a circle, a triangle, or some other two-dimensional shape. And then, we multiply by the height, also sometimes called the depth of the prism. We’ve been given in this question that the volume of this prism is 218.12 cubic metres and that the base area is 13.3 square metres. So by substituting these two values into the general formula for the volume of a prism, we have our equation. It is 218.12 is equal to 13.3ℎ.

So we’ve answered the first part of the question, which was to write an equation. And now we need to answer the second, which is to go on and solve this equation for ℎ. In order to leave ℎ on its own on the right-hand side, we need to divide by 13.3. But whatever we do to one side of an equation, we must also do to the other. On the right, dividing 13.3ℎ by 13.3 just leaves ℎ. And on the left, dividing 218.12 by 13.3 gives 16.4. So we found the height. The units for this height will be metres because the volume is given in cubic metres. And the base area was given in square metres.

Our answers then of first the equation 218.12 equals 13.3ℎ and then the height of the prism. ℎ is equal to 16.4 metres.

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