Question

Question #ff501

Answer 1

`143.7`

Explanation:

a) the first segment with `r=3cm`,
`A_1=pir^2(39/360)=pi*3^2(39/360)=0.975pi`

b) the three congruent circles with `r=3.5`cm,
`A_2=3*pir^2=3*pi*3.5^2=36.75pi`

c) the segment with `r=3.2`cm, (`angle276^@`)
`A_3=pir^2(276/360)=pi*3.2^2*(276/360)=7.85pi`

d) the small white circle with diameter `=0.8`, its radius `r=0.8/2=0.4`
`A_4=pir^2=pi*(0.4)^2=0.16pi`

Hence total coloured area `A_C=A_1+A_2+A_3-A_4`
`=> A_C=0.975pi+36.75pi+7.85pi-0.16pi =(0.975+36.75+7.85-0.16)pi =45.415pi=142.68=142.7` (one decimal place)