Respuesta :
Answer:
96%
Step-by-step explanation:
c=100=22/7D
D=7/22×100
get the radius and find the area
R=D/2
A=pi×r^2
repeat that assuming
C=140
get the area
find the %age
A2_A1=Area difference
A(diff)/A1×100=96.01%
[tex]r_{2}[/tex]Answer:
D) 96%
Step-by-step explanation:
let the circumference of circle be C = 2π[tex]r_{1}[/tex] and [tex]r_{1}[/tex] = [tex]d_{1}[/tex]/2
Initial radius (radius before increment) = [tex]r_{1}[/tex]
initial diameter (diameter before increment) = [tex]d_{1}[/tex]
Increasing the circumference of a circle other factors are constant except the radius which can be used to find the diameter hence increasing the circumference of a circle is equivalent to increasing the diameter
area of the circle before increment [tex]A_{1}[/tex] = π[tex]r_{1}[/tex]²
[tex]A_{1}[/tex] = π × ([tex]d_{1}[/tex]/2)²
[tex]A_{1}[/tex] = π[tex]d_{1}[/tex]²/4
Increment of circumference results to increment of only the diameter
diameter after increment by 40%, [tex]d_{2}[/tex] = 1.4[tex]d_{1}[/tex]
1.4 represents increment by 40%
radius after increment [tex]r_{2}[/tex] = [tex]d_{2}[/tex]/2 = 1.4[tex]d_{1}[/tex]/2 = 0.7[tex]d_{1}[/tex]
area after increment, [tex]A_{2}[/tex] = π[tex]r^{2} _{2}[/tex]
[tex]A_{2}[/tex] = π(0.7[tex]d_{1}[/tex])²
[tex]A_{2}[/tex] = π × 0.49[tex]d_{1}[/tex]²
Change in area = [tex]A_{2}[/tex] - [tex]A_{1}[/tex]
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = π × 0.49[tex]d_{1}[/tex]² - π [tex]d_{1}[/tex]²/4
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = π [tex]d_{1}[/tex]²(0.49 - ¼)
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = π [tex]d_{1}[/tex]²(0.49 - 0.25)
[tex]A_{2}[/tex] - [tex]A_{1}[/tex] = 0.24 π[tex]d_{1}[/tex]²
Percentage increment = ([tex]A_{2}[/tex] - [tex]A_{1}[/tex]/ [tex]A_{1}[/tex]) × 100
= ((0.24 π[tex]d_{1}[/tex]²)/(π[tex]d_{1}[/tex]²/4)) × 100
= (0.24 × 4 ) × 100
= 0.96 × 100
= 96 %
Hope it was useful
