A company makes two sizes of cylindrical shaped boxes. The ratio of the heights is 5:7.

What is the ratio of their volumes?

The volume ratio is also 5 : 7

Step-by-step explanation:

The volume of a cylinder is given by the following formula:

volume = pi*r²*h

Since we have two cylinders and their height varies at a ratio of 5:7 we can say that the smaller one has a height of "h" while the bigger has height of " (7/5) * h". Thefore their volume is:

volume smaller = pi*r²*h

volume bigger = pi*r² * (7/5) * h

volume bigger = (7/5) * pi*r²*h

The ratio of their volume is given by the division of the smaller volume by the bigger one:

volume ratio = volume smaller / volume bigger

volume ratio = (pi*r²*h) / [ (7/5) * pi*r²*h] = 1 / (7/5)

volume ratio = 5/7

The volume ratio is also 5 : 7.