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.
