MATH SOLVE

2 months ago

Q:
# Both circle Q and circle R have a central angle measuring 60°. The area of circle Q's sector is 9π m2, and the area of circle R's sector is 16π m2. Which is the ratio of the radius of circle Q to the radius of circle R?

Accepted Solution

A:

Answer:The ratio of the radius of circle Q to the radius of circle R is [tex]\frac{3}{4}[/tex]Step-by-step explanation:step 1Find the scale factorwe know thatIf two figures are similar, then the ratio of its areas is equal to the scale factor squaredIn this problemLetz-----> the scale factorx-----> the area of circle Q's sectory-----> the area of circle R's sectorso[tex]z^{2}=\frac{x}{y}[/tex]substitute[tex]z^{2}=\frac{9\pi}{16\pi}[/tex][tex]z^{2}=\frac{9}{16}[/tex]square root both sides[tex]z=\frac{3}{4}[/tex] ------> scale factorstep 2Find the the ratio of the radius of circle Q to the radius of circle Rwe know thatIf two figures are similar, then the ratio of its corresponding sides is equal to the scale factor In this problemThe ratio of its corresponding radius is equal to the scale factorsoLetz------> the scale factorx-----> the radius of circle Qy-----> the radius of circle Rso[tex]z=\frac{x}{y}[/tex]therefore[tex]\frac{x}{y}=\frac{3}{4}[/tex]