Question #ff501

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Question #ff501

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Answer 1 · 2016-11-07T01:53:22

$143.7$ $143.7$

Explanation:

a) the first segment with $r = 3 c m$ $r=3cm$ ,
$A_{1} = π r^{2} (\frac{39}{360}) = π \cdot 3^{2} (\frac{39}{360}) = 0.975 π$ $A_1=pir^2(39/360)=pi*3^2(39/360)=0.975pi$

b) the three congruent circles with $r = 3.5$ $r=3.5$ cm,
$A_{2} = 3 \cdot π r^{2} = 3 \cdot π \cdot {3.5}^{2} = 36.75 π$ $A_2=3*pir^2=3*pi*3.5^2=36.75pi$

c) the segment with $r = 3.2$ $r=3.2$ cm, ( $∠ 276^{\circ}$ $angle276^@$ )
$A_{3} = π r^{2} (\frac{276}{360}) = π \cdot {3.2}^{2} \cdot (\frac{276}{360}) = 7.85 π$ $A_3=pir^2(276/360)=pi*3.2^2*(276/360)=7.85pi$

d) the small white circle with diameter $= 0.8$ $=0.8$ , its radius $r = \frac{0.8}{2} = 0.4$ $r=0.8/2=0.4$
$A_{4} = π r^{2} = π \cdot {(0.4)}^{2} = 0.16 π$ $A_4=pir^2=pi*(0.4)^2=0.16pi$

Hence total coloured area $A_{C} = A_{1} + A_{2} + A_{3} - A_{4}$ $A_C=A_1+A_2+A_3-A_4$
$\Rightarrow A_{C} = 0.975 π + 36.75 π + 7.85 π - 0.16 π = (0.975 + 36.75 + 7.85 - 0.16) π = 45.415 π = 142.68 = 142.7$ $=> A_C=0.975pi+36.75pi+7.85pi-0.16pi =(0.975+36.75+7.85-0.16)pi =45.415pi=142.68=142.7$ (one decimal place)

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