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

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 $\frac{3}{2}$  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,

$\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }$

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

$\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }\\\\2 \times x = 3\\\\x = \frac{3}{2}$

Thus dimensions of cylinder A are multiplied by $\frac{3}{2}$  to produce the corresponding dimensions of cylinder B