Answer :
Answer:
The answers to each question are:
a)[tex]A=f(r=4cm)=50.26cm^2[/tex]
b)[tex]\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2[/tex]
c)[tex]C=5\cdot f(r=12.7cm)=2533.54cm^2[/tex]
d)[tex]D=f(r=28cm)+59cm^2=2522.01cm^2[/tex]
Step-by-step explanation:
The function f(r) that represents the area of a circle (in square cm) is:
[tex]f(r)=\pi r^2[/tex]
a) To represent the area (in square cm) of a circle whose radius is 4 cm, you just have to evaluate the function with a radius of 4cm:
[tex]A=f(r=4cm)=50.26cm^2[/tex]
b) To represent how much the area (in square cm) of a circle increases by when its radius increases from 10.9 to 10.91 cm, you have to represent the difference between the final area with a radius of 10.91cm and the initial area of a radius of 10.9cm:
[tex]\Delta A(10.91cm-10.9cm)=f(10.91cm)-f(10.9cm)=0.6851cm^2[/tex]
c) To represent the area of 5 circles that all have a radius of 12.7 cm, we can use the function f(r) to represent the area of a circle with a radius of 12.7cm and multiply it for 5:
[tex]C=5\cdot f(r=12.7cm)=2533.54cm^2[/tex]
d) To represent the area of the larger circle that is 59 square cm more than the first circle (with a radius of 28 cm), we can use the function f(r) to obtain the area of the first circle and addition 59 square cm:
[tex]D=f(r=28cm)+59cm^2=2522.01cm^2[/tex]
Part(a):[tex]f(r)=f(4)[/tex]
Part(b):[tex]f(10.91)-f(10.9)[/tex]
Part(c):[tex]5 f(r)=5 f(12.7)[/tex]
Part(d):[tex]28+59 =f(28)+59[/tex]
Area of the circle:
The area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula,
[tex]A= \pi r^2[/tex]
where [tex]r[/tex] is the radius of the circle
The formula for the area of the circle is,
[tex]A=\pi r^2[/tex]
Part(a):
Given,
Radius([tex]r[/tex])=4 cm
So, the area is [tex]f(r)=f(4)[/tex]
Part(b):
Given,
[tex]r=10.91\\r=10.9[/tex]
The difference in area is,
[tex]f(10.91)-f(10.9)[/tex]
Part(c):
Area of 5 circles are,
[tex]5 f(r)=5 f(12.7)[/tex]
Part(d):
The area of the larger circle is,
Area of the circle of radius [tex]28+59 =f(28)+59[/tex]
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