The ratio of the diameters of two circles is $y: z$. What is the scale factor of the circles?
A. $\frac{y}{2 z}$
B. $\frac{y}{z}$
C. $y z$
D. $2 y z$
Answer (2)
The scale factor of the circles, given the ratio of their diameters as y : z , is simply z y . Therefore, the correct answer is option B: z y . This scale factor is crucial for maintaining proportionality when comparing or resizing circular figures.
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The problem provides the ratio of the diameters of two circles as y : z .
The scale factor is the ratio of corresponding linear dimensions.
Therefore, the scale factor is z y .
The scale factor of the circles is z y .
Explanation
Analyze the problem The problem states that the ratio of the diameters of two circles is y : z . We need to find the scale factor of the circles. The scale factor is the ratio of corresponding linear dimensions of two similar figures. In this case, the diameters are the corresponding linear dimensions. Therefore, the scale factor is simply the ratio of the diameters, which is z y .
Determine the scale factor The scale factor is the ratio of corresponding linear dimensions. Since the ratio of the diameters is given as y : z , the scale factor is z y .
State the final answer Therefore, the scale factor of the circles is z y .
Examples
In architecture, when scaling blueprints of circular structures like domes or round windows, the scale factor derived from the ratio of diameters helps maintain accurate proportions in the scaled-up or scaled-down versions. For example, if you're reducing a dome's diameter from 10 meters to 5 meters, the scale factor is 10 5 = 2 1 . This ensures all other dimensions are also halved, preserving the dome's original shape and integrity.
