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.

Answer 1

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.