carlbby
Answered

the areas of the two watch faces have a ratio of 16:25. what is the ratio of the radius of the smaller watch face to the radius of the larger watch face?

Verified Answer :

Answer:

4:5

Step-by-step explanation:

Let r be the radius of small watch

Area of small watch=π\(r^{2}\)

Let R be radius of larger watch= π\(R^{2}\)

Area of larger watch= π\(R^{2}\)

It is given that the ratio of their areas= 16:25

\(\frac{ Area of smaller circe}{Area of larger circle}\)=\(\frac{16}{25}\)

π\(r^{2}\): π\(R^{2}\)= 16:25

\(\frac{r}{R}\)=\(\frac{\sqrt{16} }{\sqrt{25} }\)

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.

What is the area of the circle?

The area of the circle is given by the formula,

\(\text{Area of the Circle} = \pi r^2\)

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,

\(\text{Area of the Circle} = \pi r^2\)

Now, as we know that the ratio of the area of the watches can be written as,

\(\dfrac{\text{Area of the small watch face}}{\text{Area of the Large watch face}} = \dfrac{16}{25}\\\\\dfrac{\pi r^2}{\pi R^2} =\dfrac{16}{25}\\\\\dfrac{r^2}{R^2} = \dfrac{16}{25}\\\\\dfrac{r}{R} = \sqrt{\dfrac{16}{25}}\\\dfrac{r}{R} = \dfrac{4}{5}\)

Hence, the ratio of the radius of the smaller watch face to the radius of the larger watch face is 4:5.

Learn more about Circle:

https://brainly.com/question/11833983

Related Questions