Cylinders a and b are similar solids. the base of cylinder a has a circumference of 4r units. the base of cylinder b has an
area of 9. units
the dimensions of cylinder a are multiplied by what factor to produce the corresponding dimensions of cylinder b?

Question:

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 4π units. The base of cylinder B has an area of 9π units.The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?

Dimensions of cylinder A are multiplied by  to produce the corresponding dimensions of cylinder B

Solution:

Given that, Cylinders A and B are similar solids

The base of cylinder A has a circumference of units

The formula for the circumference of a circle is:

where, "r" is the radius of circle

r = 2

Thus, radius of cylinder A = 2 units

The base of cylinder B has an  area of units

The area of circle is given by formula:

where, "r" is the radius of circle

Thus radius of cylinder B is 3 units

Let the multiplication factor be "x"

From given,

The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B

Therefore,

Thus dimensions of cylinder A are multiplied by  to produce the corresponding dimensions of cylinder B

one set of data has more variation than the other. hope this !