Question

1) A large ball 2 m in radius is made up of a
rope of square cross section with edge
length 4 mm. Neglecting the air gaps in
the ball, what is the total length of the
rope to the nearest order of magnitude?​

Answer 1

A large ball 2m in radius is made up of a rope of square cross section with edge length 4mm. Neglecting the air gaps in the ball‚ what is the total length of the rope to the nearest order of magnitude.

solution : volume of ball = volume of rope

Let length of rope is L m

so, volume of rope = area of cross section × length of rope

= (edge length)² × L m

= (40mm)² × L m

= (40 × 10^-3 m)² × L m

= (4 × 10^-2)² × L m³

= 16 × 10^-4 × L m³

and volume of ball = 4/3 πr³

= 4/3 π (2m)³

= 4/3 π 8m³ = 32/3 π m³

now, 32/3 π m³ = 16 × 10^-4 × L m³

or, L = 32π/(3 × 16 × 10^-4)

= 2 × 3.14/3 × 10⁴

= 6.28/3 × 10⁴

= 2.093 × 10⁴ m = 2093m

Hence, length of rope = 2093m

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