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 [tex]\frac{3}{2}[/tex] 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 [tex]4 \pi[/tex] units
The base of cylinder B has an area of [tex]9 \pi[/tex] 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,
[tex]\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }[/tex]
Cylinder A:
The circumference of base of cylinder (circle ) is given as:
[tex]C = 2 \pi r[/tex]
Where "r" is the radius of circle
Given that base of cylinder A has a circumference of [tex]4 \pi[/tex] units
Therefore,
[tex]4 \pi = 2 \pi r\\\\r = 2[/tex]
Thus the dimension of cylinder A is radius = 2 units
Cylinder B:
The area of base of cylinder (circle) is given as:
[tex]A = \pi r^2[/tex]
Given that, the base of cylinder B has an area of [tex]9 \pi[/tex] units
Therefore,
[tex]\pi r^2 = 9 \pi\\\\r^2 = 9\\\\r = 3[/tex]
Thus the dimension of cylinder B is radius = 3 units
[tex]\text{Dimensions of cylinder A} \times x = \text{Dimensions of cylinder B }\\\\2 \times x = 3\\\\x = \frac{3}{2}[/tex]
Thus dimensions of cylinder A are multiplied by [tex]\frac{3}{2}[/tex] to produce the corresponding dimensions of cylinder B
