Question

iv) 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

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.