Question

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

Answer 1

Answer:

Length is 2093 m.

Explanation:

We know that the volume of ball = volume of rope from the question.

Now, if we let length of rope to be L m.

Hence, rope's volume will be = cross sectional area ×rope length.

= (edge length)^2 × L m.

= (40mm)^2 × L m.

= (40 × 10^-3 m)^2 × L m.

= (4 × 10^-2)^2 × L m^3.

= 16 × 10^-4 × L m^3.

We know that spher volume or volume of ball = 4/3 πr^3.

= 4/3 π (2m)^3.

= 4/3 π 8m^3 = 32/3 π m^3

Now, 32/3 π m^3 = 16 × 10^-4 × L.

So, L = 32π/(3 × 16 × 10^-4).

= 2 × 3.14/3 × 10^4.

= 6.28/3 × 10^4.

= 2.093 × 10^4 m = 2093m

So, from the above calculations the length of rope will be = 2093m.