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?

Answer 1

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 $\frac{3}{2}$.

Answer 2

The base of cylinder b has an are of 9 unites