Chapter 12.7, Problem 25IP

a)

To determine

To find : Volume of empty space.

Answer to Problem 25IP

  $140.45c{m}^3$

Explanation of Solution

Given Information :

The given information is, as figure given in question

  

Length (l) = $13.1$ cm, breadth (b) = $4.5$ cm and height (h) = $4.5$ cm

Each ball is $4.3$ centimeters diameters.

Radius = $\frac{4.3}{2}$ cm

Formula Used:

Volume of cuboid = l × b × h

Volume of sphere = $\frac{4}{3}\pi r^3$

Calculation :

Volume of cuboid = $(13.1)(4.5)(4.5)$

  $=265.275c{m}^3$

Volume of $3$ spheres = $3\times \frac{4}{3}\times (3.14)\times \frac{{(4.3)}^3}{2}$

  $\begin{array}{l}=4\times (3.14)\frac{{(4.3)}^3}{2}\\ =124.83c{m}^3\end{array}$

So, empty space in volume = $(265.28-124.83)c{m}^3$

  $=140.45c{m}^3$

b)

To determine

To find : How much percentage of box is full.

Answer to Problem 25IP

  $47.05\%$

Explanation of Solution

Given Information :

The given information is, Volume of box = $265.28c{m}^3$

Formula Used:

Volume of cuboid = l × b × h

Calculation :

Percentage of box is full = $\frac{\text{Volumeof 3 spheres}}{\text{Volume of box}}\times 100$

  $\begin{array}{l}=\frac{124.83}{265.28}\times 100\\ =47.05\%\end{array}$