Question

iv) A large ball 2 m in radius is made up of
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

Answer:

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