Question

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

Answer 1

Answer:

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.