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Question
The diameters of three wheels are in the ratio 2 : 4 : 8. If the sum of the circumferences of these circles be 132 cm, find the difference between the areas of the largest and the smallest of these wheels.
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Solution
Let the diameters of three wheel be
d1 = 2x ⇒ r1 = x
d2 = 4x ⇒ r2 = 2x
d3 = 8x ⇒ r3 = 4x
Now,
2πr1 + 2πr2 + 2πr3 = 132
⇒ 2π(r1 + r2 + r3) = 132
⇒ x + 2x + 4x = `66 xx (7)/(22)`
⇒ 7x = 21
⇒ x = 3cm
∴ DIfference between the areas of the largest and the smallest wheels
= πr32 - πr12
= π(4 x 3)2 - π(3)2
= 144π - 9π
= 135π
= `135 xx (22)/(7)`
= 424.29cm2.
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