Chapter 12.5, Problem 41STP

To determine

To determine how many cubic centimeter of sand will it hold when it is filled to the top.

Answer to Problem 41STP

  $12\pi {\text{ centimeter}}^3$ or option(a)

Explanation of Solution

Given:

  

Formula used:

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

  $\left[r=\text{Radius, }h\text{=}\text{height}\right]$

Slant height, $l=\sqrt{{\text{radius}}^2+{\text{height}}^2}$

Calculation:

Given figure,

  

Slant height of cone $=5\text{ centimeter}$

Height of cone $=4\text{ centimeter}$

Slant height can be represented as $l$ , height is $h$ and radius $r$ .

  $\Rightarrow l=\sqrt{r^2+h^2}$

  $\Rightarrow r=\sqrt{l^2-h^2}$

  $\Rightarrow r=\sqrt{{(5)}^2-{(4)}^2}$

  $\Rightarrow r=\sqrt{9}$

  $\Rightarrow r=3$ Centimeter

Now volume of the cone,

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

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

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times 9\times 4$

  $\Rightarrow$ Volume of the cone $V=12\pi {\text{ centimeter}}^3$

Conclusion:

Therefore, $12\pi {\text{ centimeter}}^3$ or option(a) of sand will it hold when it is filled to the top.