Chapter 12, Problem 16MCQ

To determine

To calculate:To find the amount of frosting that can fit in a bag

Answer to Problem 16MCQ

Amount of frost that can fit in bag is $37.7i{n}^3$

Explanation of Solution

Given information: Bag has diameter of $4$ inches and height of $9$ inches and bag is in shape of cone

Formula Used:

Volume of cone is given by the below formula:

  $Volume=\frac{1}{3}\pi r^{2}h$

Where,

  $r=$ Radius of cone

  $h=$ Height of cone

Calculation:

Given a bag has diameter of $4$ inches and height of $9$ inches and bag is in shape of cone

  $\begin{array}{l}r=\frac{Diameter}{2}=\frac{4}{2}=2in.\\ h=9in.\end{array}$

Amount of frosting that can fit in the conical bag is equal to the volume of the conical bag

Volume of cone is calculated as follows:

  $Volume=\frac{1}{3}\pi r^{2}h$

Substituting the values, volume is

  $\begin{array}{l}Volume=\frac{1}{3}\times \frac{22}{7}\times {\left(2\right)}^2\times 9\\ Volume=\frac{1}{1}\times \frac{22}{7}\times 2\times 2\times 3\\ Volume=37.7i{n}^3\end{array}$

Conclusion:

Hence, amount of frost that can fit in bag is $37.7i{n}^3$