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ipn [44]
3 years ago
9

Both circle Q and circle R have a central angle measuring 140°. The area of circle Q's sector is 25π m2, and the area of circle

R's sector is 49π m2. Which is the ratio of the radius of circle Q to the radius of circle R?
Mathematics
2 answers:
taurus [48]3 years ago
7 0

Solution:

we are given that

Both circle Q and circle R have a central angle measuring 140°. The area of circle Q's sector is 25π m^2, and the area of circle R's sector is 49π m^2.

we have been asked to find the ratio of the radius of circle Q to the radius of circle R?

As we know that

Area of the sector is directly proportional to square of radius. So we can write

Area  \  \   \alpha \ \  r^2\\ \\ \Rightarrow A=kr^2\\ \\ \text{where k is some proportionality constant }\\ \\ \Rightarrow \frac{A_1}{A_2}=\frac{r_1^2}{r_2^2}\\ \\  \Rightarrow \frac{r_1^2}{r_2^2}=\frac{A_1}{A_2}\\ \\  \Rightarrow \frac{r_1^2}{r_2^2}=\frac{25 \pi}{49 \pi}\\ \\  \Rightarrow \frac{r_1}{r_2}=\sqrt{\frac{25 \pi}{49 \pi}} \\ \\  \Rightarrow \frac{r_1}{r_2}=\frac{5}{7} \\


seropon [69]3 years ago
6 0
The answer will be 5/7
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