SOLUTION: Hi, I have answered these questions but I'm not sure of my answers, can you check them please? thanks! 1. Given triangle JKL~triangle PQR and KL=3/4QR. Which of the following is

Question 1163388: Hi, I have answered these questions but I'm not sure of my answers, can you check them please? thanks!
1. Given triangle JKL~triangle PQR and KL=3/4QR. Which of the following is true?
a. The ratio of areas of triangle JKL to PQR is 9/16
b. Angle K=3/4 of angle Q
c. The ratio of perimeters of triangle PQR to triangle JKL is 3/4
d. None of the above
I'm stuck between b and c
2. A water glass is shaped like a cylinder with height 9 in. and diameter 4 in. How many times as much water
can a glass twice as tall and twice as wide hold?
a.18
b.4
c.8 -> my answer
d.16
3. A circle with a radius of 8 is placed within a square (the radius of the square is also 8), the square is shaded. Find the probability that a random point is within the shaded region. Express your answer as percent to the
nearest tenth.
a.21.5%
b.27.3%
c.72.7%
d.78.5% -> my answer
4.A rectangle with the dimensions of 10 by 4 is placed within a bigger rectangle with dimensions 6 by 16, the bigger rectangle is shaded. Find the probability that a randomly selected point falls in the shaded region.
a. 56.0%
b. 58.3%
c. 71.4%
d. 41.7% -> my answer I got 0.4117
5. Two similar cylinders have heights of 2 cm and 3 cm. What is the ratio of their volumes?
a. 4/9
b. 8/27
c. 2/3 --> my answer
d. 1/2
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

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.

Angles of similar figures are congruent; making a figure larger or smaller while keeping the same shape does not change angles.

So....

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.

2. We're talking volume here; the scale factor is 2:1, so the volume ratio is 8:1
answer c; you are correct

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.

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.

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.

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