Question

A ball is made of a long string of thickness about 2 mm. The radius of the ball is 10 cm. Estimate the length of the string. Point out the possible errors in your calculation.

Answer 1

As the ball was made from the string, the volume of the ball must be equal to the volume of the string.

If we assume that the string is a long cylinder, we get

$$V_{ball}=V_{string}$$ $$\frac{4}{3}\pi R^3=\pi\frac{d^2}{4}L$$ $$L=\frac{16R^3}{3d^2}=\frac{16*0.1^3}{3*0.002^2}=1333.3 m$$

Answer: Length of the string 1333.3m

The possible source of error is the assumption that the string is cylindrical.