Answer:
4:5
Step-by-step explanation:
Let r be the radius of small watch
Area of small watch=π[tex]r^{2}[/tex]
Let R be radius of larger watch= π[tex]R^{2}[/tex]
Area of larger watch= π[tex]R^{2}[/tex]
It is given that the ratio of their areas= 16:25
[tex]\frac{ Area of smaller circe}{Area of larger circle}[/tex]=[tex]\frac{16}{25}[/tex]
π[tex]r^{2}[/tex]: π[tex]R^{2}[/tex]= 16:25
[tex]\frac{r}{R}[/tex]=[tex]\frac{\sqrt{16} }{\sqrt{25} }[/tex]
r:R= 4:5
Hence, the ratio of their radii= 4:5
Hence, the correct answer is 4:5
The ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.
The area of the circle is given by the formula,
[tex]\text{Area of the Circle} = \pi r^2[/tex]
As we know that the ratio of the area of the two watches is 16:25. And we also know that the area of a circle is given by the formula,
[tex]\text{Area of the Circle} = \pi r^2[/tex]
Now, as we know that the ratio of the area of the watches can be written as,
[tex]\dfrac{\text{Area of the small watch face}}{\text{Area of the Large watch face}} = \dfrac{16}{25}\\\\\dfrac{\pi r^2}{\pi R^2} =\dfrac{16}{25}\\\\\dfrac{r^2}{R^2} = \dfrac{16}{25}\\\\\dfrac{r}{R} = \sqrt{\dfrac{16}{25}}\\\dfrac{r}{R} = \dfrac{4}{5}[/tex]
Hence, the ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.
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