Help with Operations on Functions

[Figure_skater123]

I was wondering if someone could help me with this question. i am working with Operations on Functions. I was just working if i was doing this correctly.

Let r centimeters represent the radius of a compact disc, measured from the center of the hole. The radius of the hole itself is r/8 centimeters.

a) Write a function to represent the area, A(r), of one side of the compact disc, including the hole.

a(r) = ½ x 3.14 x r2

b) Write a function to represent the area, B(r), of the hole.

B(r) = 3.14 x r^2
(3.14)(r/8)^2

c) Write and simplify a function, C(r), to represent the area of one side of the disc, excluding the hole.

(A-B)(r) = (1/2 x 3.14 x r^2) - (3.14 x (r/8)^2)

d) If r represents 6 cm, what is the area of one side of the disc, excluding the hole, to the nearest square centimeter?

(A-B)(r) = (1/2 x 3.14 x r^2) - (3.14 x (r/8)^2)
= (1/2 x 3.14 x 6^2) - (3.14 x (6/8)^2)
= (.5 x 3.14 x 36) - (3.14 x .5625)
= 56.52 - 1.76625
= 54.75375


I don't think I am doing this right so could someone help me please?

 

[Gene]

a)
a(r) = ½ x 3.14 x r2
A(r) = pi*r^2 IS the area of one side.

b)
B(r) = 3.14 x r^2
(3.14)(r/8)^2
B(r) = pi*(r/8)^2 is correct.

c)
(A-B)(r) = (1/2 x 3.14 x r^2) - (3.14 x (r/8)^2)
C(r) = pi*r^2*(1-(1/8)^2) =
pi*r^2*(63/64) is simpler.

d)
(A-B)(r) = (1/2 x 3.14 x r^2) - (3.14 x (r/8)^2)
= (1/2 x 3.14 x 6^2) - (3.14 x (6/8)^2)
= (.5 x 3.14 x 36) - (3.14 x .5625)
= 56.52 - 1.76625
= 54.75375
B(r) = pi*6^2(63/64) =
111 is correct to the nearest square centimeter.

Your only real mistake was that stray 1/2 and not rounding in the last (corrected) line. If you wanted both sides it would be 2*pi*r^2.

 

[Figure_skater123]

Oh ok, I knew I was doing it wrong but i didn't know exactly what I was doing wrong. Thank you for you help.