Respuesta :
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:
Given that, Cylinders A and B are similar solids
The base of cylinder A has a circumference of [tex]4 \pi[/tex] units
The formula for the circumference of a circle is:
[tex]C = 2 \pi r[/tex]
where, "r" is the radius of circle
[tex]4 \pi = 2 \pi r[/tex]
r = 2
Thus, radius of cylinder A = 2 units
The base of cylinder B has an area of [tex]9 \pi[/tex] units
The area of circle is given by formula:
[tex]Area = \pi r^2[/tex]
where, "r" is the radius of circle
[tex]9 \pi = \pi r^2\\\\r^2 = 9\\\\r = 3[/tex]
Thus radius of cylinder B is 3 units
Let the multiplication factor be "x"
From given,
The dimensions of cylinder A are multiplied by what factor to produce the corresponding dimensions of cylinder B
Therefore,
[tex]Radius\ of\ Cylinder\ A = x \times Radius\ 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
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