Answer:
The factor is [tex]\frac{3}{2}[/tex].
Step-by-step explanation:
Given : Cylinders A and B are similar solids.
The base of cylinder A has a circumference of [tex]4\pi[/tex] units.
The base of cylinder B has an area of [tex]9\pi[/tex] 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,
[tex]\text{Dimension of cylinder A}\times x = \text{Dimension of cylinder B}[/tex] ........[1]
The dimension refer here are radius of both cylinders.
In cylinder A,
Circumference of base is [tex]4\pi[/tex] units.
Circumference of base of cylinder is [tex]C=2\pi r[/tex]
[tex]4\pi=2\pi r[/tex]
[tex]r=2[/tex]
The dimension of cylinder A is r=2
In cylinder B,
Area of cylinder is [tex]9\pi[/tex] units.
Area of base of cylinder is [tex]A=\pi r^2[/tex]
[tex]9 \pi=\pi r^2[/tex]
[tex]r^2=9[/tex]
[tex]r=3[/tex]
The dimension of cylinder B is r=3
Substitute in [1]
[tex]2x=3[/tex]
[tex]x=\frac{3}{2}[/tex]
Therefore, The factor is [tex]\frac{3}{2}[/tex].
