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
Answers
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
Answer:10^3 km
Explanation: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