Question

Cylinders A and B are similar solids. The base of cylinder A has a circumference of 47 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?

Answer 1

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:

Dimensions of cylinder A are multiplied by
`(3)/(2)` to produce the corresponding dimensions of cylinder B

Solution:

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

Let "x" be the required factor

From given question,

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

Therefore, we can say,

`\text{Dimensions of cylinder A} * x = \text{Dimensions of cylinder B }`

Cylinder A:

The circumference of base of cylinder (circle ) is given as:

`C = 2 \pi r`

Where "r" is the radius of circle

Given that base of cylinder A has a circumference of
`4 \pi` units

Therefore,

`4 \pi = 2 \pi r\\\\r = 2`

Thus the dimension of cylinder A is radius = 2 units

Cylinder B:

The area of base of cylinder (circle) is given as:

`A = \pi r^2`

Given that, the base of cylinder B has an area of
`9 \pi` units

Therefore,

`\pi r^2 = 9 \pi\\\\r^2 = 9\\\\r = 3`

Thus the dimension of cylinder B is radius = 3 units

`\text{Dimensions of cylinder A} * x = \text{Dimensions of cylinder B }\\\\2 * x = 3\\\\x = (3)/(2)`

Thus dimensions of cylinder A are multiplied by
`(3)/(2)` to produce the corresponding dimensions of cylinder B