Chapter 12.4, Problem 4CYP

To determine

To find:

The how many times as much popcorn does the larger container hold.

Answer to Problem 4CYP

The option G is true.

Explanation of Solution

Given information:

  

Calculation:

Smaller tanker has diameter $14.5\text{ cm}$ and height $18\text{ cm}$ .

Smaller tanker has radius $\frac{14.5}{2}=7.25\text{ cm}$ .

Volume of smaller tanker is:

  $\begin{array}{c}V=\pi r^{2}h\\ =\pi {\left(7.25\right)}^{2}18\\ =\pi \left(52.5625\right)18\\ =946.125\pi \\ =2973.53{\text{ cm}}^3\end{array}$

Larger tanker has diameter $\text{22}\text{.8 cm}$ and height $18\text{ cm}$ .

Larger tanker has radius $\frac{22.8}{2}=11.4\text{ cm}$ .

Volume of larger tanker is:

  $\begin{array}{c}V=\pi r^{2}h\\ =\pi {\left(11.4\right)}^{2}18\\ =\pi \left(129.96\right)18\\ =946.125\pi \\ =2973.53{\text{ cm}}^3\end{array}$

So, approximately $2.5$ times as much popcorn fill in the large container than smaller container.

Hence, option G is true.