Chapter 12.5, Problem 23PPS

To determine

To determine how much cubic centimeter of roasted peanut can fill the paper cone.

Answer to Problem 23PPS

  $V=234.6$ centimeter

Explanation of Solution

Given:

Height of the cone $=14$ centimeter

Base diameter $=8$ centimeter

Formula used:

Volume of the cone, $V=\frac{1}{3}\pi r^{2}h$

Calculation:

The paper cone has height of $14$ centimeter and base diameter $8$ centimeter,

So, the radius of the base is $=\frac{\text{Diameter}}{2}$

  $\Rightarrow$ Radius of the base $=\frac{\text{Diameter}}{2}=\frac{8}{2}=4$ centimeter

Now to fill up the cone considering the volume of the paper cone,

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\pi r^{2}h$

Putting the values of $r=4$ centimeter and $h=14$ centimeter,

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(4)}^2\times 14$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times 16\times 14$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 703.716$

  $\Rightarrow$ Volume of the cone $V=234.572$

Rounding off to nearest tenth,

  $\Rightarrow$ Volume of the cone $V=234.6$

Conclusion:

Therefore, the cubic centimeter of roasted peanut can fill the paper cone is $V=234.6$ centimeter.