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प्रश्न
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.
उत्तर
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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