The answer is 1:9
Explanation:
Step 1 :
Given the radius of cylinder A is 3 times the radius of cylinder B.
we know the formula for a cylinder's volume,
The Volume of the cylinder (V) = πr²h
Step 2 :
Let r be the radius of cylinder B, then the radius of cylinder A is 3r
substituting the values of the radius in the above equation we get,
The volume of cylinder A = π.(3r²)·h
=(9)(π). (r²) .h
Tripling the radius in cylinder A the volume becomes 9 times the volume of cylinder B. The height of cylinder A must be 1/9 the height of cylinder B, if the volumes are to be the same.
ANSWER: The ratio of the heights of cylinders A and B is 1:9.