Question 1163388
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In similar figures, if the ratio of corresponding linear measurements (scale factor) is a:b, then the ratio of corresponding area measurements is a^2:b^2, and the ratio of corresponding volume measurements is a^3:b^3.<br>
Angles of similar figures are congruent; making a figure larger or smaller while keeping the same shape does not change angles.<br>
So....<br>
1. The scale factor is 3:4
a. Yes; the ratio of areas is 3^2:4^2 = 9:16
b. No
c. Yes; perimeter is a linear measurement
a and c are both right answers.<br>
2. We're talking volume here; the scale factor is 2:1, so the volume ratio is 8:1
answer c; you are correct<br>
3. The description is unclear; a square doesn't have a radius, and I don't now where the shading is.  If the figure is a circle inscribed in a square (diameter of circle equal to side of square), then the probability that a random point is INSIDE the circle is the ratio of the areas of the circle and square, which is pi/4 = .7854 = (approximately) 78.5% -- answer c.  But from the description it sounds as if the question asks for the probability that the random point is inside the square but OUTSIDE the circle; that of course would be 1-pi/4 = 21.5%, which is answer a.<br>
4. Again I can't see the shading.  The area of the large rectangle is 96; the area of the small one is 40.  The probability that a random point in the large rectangle is also inside the smaller rectangle is 40/96 which gives answer d, 41.7%.  The question might be asking for the probability that the point in the larger rectangle is NOT inside the smaller rectangle; then of course the answer would be 100%-41.76% = 58.3%, which is answer b.<br>
5. This one is straightforward.  Height is a linear measurement; the scale factor is 2:3.  The ratio of volumes is 2^3:3^3 = 8:27, answer b.<br>