a We are told that the cross section of a balloon that is used to dilate the coronary artery is a circle. Here is the diameter of the balloon before and after the inflation.
Before:& 1.5 mm
After:& 2 mm
We see that the dilation is an enlargement because the diameter of becomes larger than it was before. Let's also remember that the scale factor of a dilation is the ratio of a length in the image to the corresponding length in the preimage.
k=image length/preimage length
Here the diameter of the image is 2 mm and the diameter of the preimage is 1.5mm. Let's substitute them into the formula.
b We want to find the area of the cross-section of the balloon before and after dilation. First, we know that the cross-section of the balloon is a circle. Let's then remember the formula for the area of a circle.
A = π r^2Let's first find A_1, which is the area of the cross-section before the dilation. See that the cross-section has a radius of 1.5 mm2, or 0.75 mm.
Before the dilation, the cross-sectional area of the balloon was about 1.77mm^2. To find the other area, we should substitute 2 mm2, or 1 mm, for r in the formula for the area of a circle.
