Question

I’m supposed to put theses least to greatest according to their volumes assume the variable h has the same value for each figure

Answer 1

Hello there. To solve this question, we'll have to remember some properties about finding volumes of polyhedrons.

Given the following figures, we have to order them from least to greatest with respect to volume:

In this case, as h is the same for all the polyhedrons, we simply have to compare their volumes with respect to the constant multiplying h.

For a cylinder of radius r and height h, its volume is given by:

`V_{\text{cylinder}}=\pi\cdot r^2\cdot h`

For a cone with radius r and height h, its volume is given by:

`V_{\text{cone}}=(\pi\cdot r^2\cdot h)/(3)`

Labelling each of the figures (go back to the image), we calculate their volume as follows:

Since h is the same, we compare the constants. We know that pi is approximately equal to 3.14, therefore:

The order we have to put these figures is 3, 4, 2, 1.