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?
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Here the total length of the rope can be given by the surface area of the ball.
Surface area of the ball is,
4π × 2² = 16π m²,
because the surface area of a sphere is 4πr².
We can get that, the area of one lengthy side of a rope gives the surface area for the ball. The other lengthy side comes inside the ball.
Given that the edge length of the rope is 4 mm, i.e., 4 × 10^(-3) m.
So the area of one lengthy side of the rope is,
4 × 10^(-3) × L m²,
where L is the total length of the rope.
Now,
4 × 10^(-3) × L = 16π
L = 4π × 10³ m
Taking π = 3.14,
L = 4 × 3.14 × 10³ m
L = 12.56 × 10³ m
L = 1.256 × 10⁴ m
The final answer is for getting it to the nearest order of magnitude. Here it's 4.
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