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defon
3 years ago
12

Both circle Q and circle R have a central angle measuring 75°. The ratio of circle Q's radius to circle R's radius is 2:5. Which

ratio represents the area of the sector for circle R to the area of the sector for circle Q?
Mathematics
2 answers:
ycow [4]3 years ago
7 0
The ratio of similar areas is the square of the ratio of the scale factor.

Circle R's sector is (5/2)² = 25/4 the area of Circle Q's sector.
Lynna [10]3 years ago
7 0

Answer:

The ratio of the area of the sector for circle R to the area of the sector for circle Q is 25:4.

Step-by-step explanation:

Given information: Q are R different circles. The ratio of circle Q's radius to circle R's radius is 2:5.

Let the radius of Q and R are 2x and 5x respectively.

The central angle of each circle is 75°.

The area of a sector is

A=\pi r^2(\frac{\theta}{360^{\circ}})

where, r is the radius of circle and θ is central angle of sector.

Area of sector of circle Q.

A_Q=\pi (2x)^2(\frac{75^{\circ}}{360^{\circ}})

Area of sector of circle R.

A_R=\pi (5x)^2(\frac{75^{\circ}}{360^{\circ}})

The ratio of area of sector for circle R to the area of the sector for circle Q is

\frac{A_R}{A_Q}=\frac{\pi (5x)^2(\frac{75^{\circ}}{360^{\circ}})}{\pi (2x)^2(\frac{75^{\circ}}{360^{\circ}})}

\frac{A_R}{A_Q}=\frac{25x^2}{4x^2}

\frac{A_R}{A_Q}=\frac{25}{4}

Therefore the ratio of the area of the sector for circle R to the area of the sector for circle Q is 25:4.

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