Question

question 7 (multiple choice worth 1 points)
(scale factor and dilation lc)
a larger cylinder is a dilation of a smaller cylinder.
what is the scale factor, ( k )?
( k = 20 )
( k = 17.5 )
( k = 8 )
( k=\frac{1}{8} )

Explanation:

Step1: Recall the formula for scale factor

The scale factor \(k\) for a dilation is given by \(k=\frac{\text{dimension of image}}{\text{dimension of pre - image}}\). Here, the dimension is the radius.

Step2: Substitute the values

The radius of the image (larger cylinder) \(r_{image}=20\) m and the radius of the pre - image (smaller cylinder) \(r_{pre - image}=2.5\) m. So, \(k = \frac{20}{2.5}\).

Step3: Calculate the value

\(k=\frac{20}{2.5}=\frac{20\times10}{2.5\times10}=\frac{200}{25}=8\)

Answer:

\(k = 8\) (corresponding to the third option)