Chapter 12.6, Problem 32PPS

To determine

Calculate the size of the balloon that could lift a person who weighs $65$ kg.

Answer to Problem 32PPS

The diameter of the balloon will be $139,286cm$ .

Explanation of Solution

Given:

It is given in the question that there is a spherical helium − filled balloon with a diameter of $30$ cm can lift a $14$ gram objects.

Concept Used:

In this, use the concept of proportion of weight to the diameter i.e. $\frac{w_1}{d_1}=\frac{w_2}{d_2}$ .

Calculation: Here, $d_1=30cm,w_1=14gram,w_2=65kg=65,000gram$

Now, using the proportion,

  $\begin{array}{l}\frac{w_1}{d_1}=\frac{w_2}{d_2}\\ \frac{14}{30}=\frac{65000}{d_2}\\ 14\cdot d_2=65000\cdot 30\\ d_2=\frac{65000\times 30}{14}\\ d_2=139,286cm\end{array}$

Conclusion:

The diameter will be $139,286cm$ .