Answer:
The factor is \(\frac{3}{2}\).
Step-by-step explanation:
Given : Cylinders A and B are similar solids.
The base of cylinder A has a circumference of \(4\pi\) units.
The base of cylinder B has an area of \(9\pi\) units.
To find : The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B?
Solution :
Let x be the factor.
So, according to question,
\(\text{Dimension of cylinder A}\times x = \text{Dimension of cylinder B}\) ........[1]
The dimension refer here are radius of both cylinders.
In cylinder A,
Circumference of base is \(4\pi\) units.
Circumference of base of cylinder is \(C=2\pi r\)
\(4\pi=2\pi r\)
\(r=2\)
The dimension of cylinder A is r=2
In cylinder B,
Area of cylinder is \(9\pi\) units.
Area of base of cylinder is \(A=\pi r^2\)
\(9 \pi=\pi r^2\)
\(r^2=9\)
\(r=3\)
The dimension of cylinder B is r=3
Substitute in [1]
\(2x=3\)
\(x=\frac{3}{2}\)
Therefore, The factor is \(\frac{3}{2}\).
