Answer:
a) 220.17 cm
b) 2127.12 cm²
Step-by-step explanation:
perimeter = circumference
it is the sum of the inner and the outer arc and the 2 side lines of 25.
we know a full circle has 360 degrees. but we only look at a segment of a circle of 150 out of the total of 360 degrees.
the circumference of a circle is
C = 2×pi×r
the 150 degree part is then
C = 2×pi×r×150/360 = 2×pi×r×15/36 = pi×r×15/18 =
= pi×r×5/6
the radius of the inner circle is 20.
=>
Ci = pi×20×5/6 = pi×50/3
the radius of the outer circle is 20 + 25 = 45
Co = pi×45×5/6 = pi×75/2
so, the total perimeter/ circumference is
C = Ci + Co + 25 + 25 = pi×50/3 + pi×75/2 + 50
= pi×100/6 + pi×225/6 + 50 = pi×325/6 + 50 =
= 220.17 cm
the area of the shaded shape is the area of the large circle segment minus the area of the small circle segment.
the area of a circle is
A = pi×r²
the 150 degree part is then
A = pi×r²×150/360 = pi×r²×5/12
so, for the inner circle that is
Ai = pi×20²×5/12 = pi×400×5/12 = pi×100×5/3 = pi×500/3
for the outer circle that is
Ao = pi×45²×5/12 = pi×2025×5/12 = pi×10125/12 =
= pi×3375/4
so, the total area of the shaded shape is
A = Ao - Ai = pi×3375/4 - pi×500/3 = pi×(10125-2000)/12 =
= pi×8125/12 = 2127.12 cm²
