Answer:
a) x = 6
b) 0.2 radians.
Step-by-step explanation:
I ran out of time and the system logged me out so I'll start again:
a) Find the lengths of the arcs in terms of x and Ф:
arc SP = radius * Ф = 10Ф
arc TS = 10*3Ф = 30Ф
arc PT = 10Ф+30Ф = 40Ф.
arc QR = (10 + x)Ф
QR/PT = 2/5 so:
2/5 = (10 + x)Ф / 40Ф
Cross multiply:
80Ф = 50Ф + 5xФ
5xФ = 30Ф
x = 6.
b)
The area of a sector = radius^2 * angle in radians.
The shaded area = area of arc QOR - area of arc POS:
31.2 = (10 + x)^2 Ф - 10^2 Ф
x = 6 so:
16^2 Ф - 100 Ф = 31.2
Ф = 31.2 / 156
= 0.2 radians.
