# CAT Practice : Mensuration

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What is the relation between length of the string and a Circle ( p.s. it has something do with the circumference!!).

## Length of String

Q.6: A string is wound around two circular disk as shown. If the radius of the two disk are 40 cm and 30 cm respectively. What is the total length of the string?

1. 70 cm
2. 70 + 165*${\pi}$
3. 70 + 120${\pi}$
4. 70 + 165*${\frac {\pi}{2}}$

Choice D. 70 + 165*${\frac {\pi}{2}}$

## Detailed Solution

As, tangent from an exterior point makes right angle with the radius.

=) ADXB and ODX’E are squares,

∴ AO = BO = 40 cm

OD = DE = 30 cm

Length of string wound around circle x =)${\frac {270°}{360°} * 2 * \pi * 80}$

= ${\frac {3}{4} * 80\pi}$

=60${\pi}$

Similarly, Length of string wound around circle x’ =)${\frac {270°}{360°} * 2 * \pi * 30}$

= ${\frac {3}{4} * 30\pi}$

= ${\frac {45}{2} * \pi}$

∴ Length of the string = 40 + 30 + 60π + ${\frac {45}{2} * \pi}$

= 70 + 165*${\frac {\pi}{2}}$

Choice (D) is therefore, the correct answer.

Correct Answer: 70 + 165*${\frac {\pi}{2}}$

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## More questions from Mensuration

Mensuration is the science of measurement. Cylinders, cones, cuboids, rectangular parallelopipeds etc.