Explanation:
To find the factor by which the dimensions of cylinder A were multiplied to produce the corresponding dimensions of cylinder B, we can use the fact that they are similar solids. This means that the ratio of corresponding dimensions is the same for both cylinders.
Since the base of cylinder A has a circumference of 4π units and the base of cylinder B has an area of 9π units, we can use these measurements to find the ratio of the radii of the two cylinders.
The circumference of a circle is given by 2πr, where r is the radius, so the radius of cylinder A is 4π/2π = 2 units.
The area of a circle is given by πr^2, so the radius of cylinder B is sqrt(9π/π) = sqrt(9) = 3 units.
The ratio of the radius of cylinder A to cylinder B is 2/3. Since similar solids have the same ratio for all dimensions, this means that the dimensions of cylinder A were multiplied by a factor of 2/3 to produce the corresponding dimensions of cylinder B.