Respuesta :
The ratio of the area of circle A to the area of circle B for the considered circle A and B is 100:64
What is the ratio of two quantities?
Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unitless(no units) quantity.
Let we suppose that:
- The radius of circle A = C units
- The radius of circle B = s units.
Then we get:
- Circumference of circle A = [tex]2\pi r \: \rm units[/tex]
- Circumference of circle B = [tex]2\pi s \: \rm units[/tex]
As per the given information:
The circumference of a circle B is 80% of the circumference of circle A, or:
[tex]2\pi s \: \rm units[/tex] = 80% of [tex]2\pi r \: \rm units[/tex]
or:
[tex]2\pi s = \dfrac{2\pi r}{100} \times 80\\\\s = 0.8r \: \rm units[/tex]
Also, we have:
- Area of circle A = [tex]\pi r^2 \: \rm units[/tex]
- Area of circle B = [tex]\pi s^2 \: \rm units[/tex]
The rato of the area of the circle A to the area of the circle B is:
[tex]Area(A): Area(B) = \dfrac{\pi r^2}{\pi s^2} = \left( \dfrac{r}{s}\right)^2[/tex]
since we've got [tex]s= 0.8r[/tex], therefore,
[tex]Area(A): Area(B)= \left( \dfrac{r}{s}\right)^2 = \left(\dfrac{r}{0.8r}\right)^2 = \dfrac{100}{64} \\\\Area(A): Area(B)=\dfrac{100}{64} = 100:64[/tex]
Thus, the ratio of the area of circle A to the area of circle B for the considered circle A and B is 100:64
Learn more about ratio here:
brainly.com/question/186659
