Chapter 12.5, Problem 28PPS

To determine

To determine the volume of each solid figure

Answer to Problem 28PPS

  $5574.8{\text{ centimeter}}^3$

  $7698.5{\text{ centimeter}}^3$

Explanation of Solution

Given:

  

Formula used:

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

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

Volume of cylinder $=\pi r^2\text{h }\left[r\text{= radius, }h\text{= height}\right]$

Calculation:

The given figure,

  

Splitting the image in two parts,

  

Taking part I:

  

Height of the cone $=12$ centimeter

Diameter of the base $=26$ centimeter

Radius of the base $=\frac{\text{Diameter}}{2}=\frac{26}{2}=13$ centimeter

Now, volume of the cone,

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

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times \pi \times {(13)}^2\times 12$

  $\Rightarrow$ Volume of the cone $V=\frac{1}{3}\times 6371.1499$

  $\Rightarrow$ Volume of the cone $V=2123.7166{\text{ centimeter}}^3$

Rounding off to nearest tenth,

  $\Rightarrow$ Volume of the cone $V=2123.7{\text{ centimeter}}^3$

Taking part II:

  

Diameter of the cylinder $=26$ centimeter

Radius of the cylinder $=\frac{\text{Diameter}}{2}=\frac{26}{2}=13$ centimeter

Height of the cylinder $=10.5$ centimeter

Now, volume of the cylinder,

  $\Rightarrow$ Volume of the cylinder $=\pi \times {(13)}^2\times 10.5$

  $\Rightarrow$ Volume of the cylinder $=5574.7561{\text{ centimeter}}^3$

Rounding off to nearest tenth,

  $\Rightarrow$ Volume of the cylinder $=5574.8{\text{ centimeter}}^3$

Total volume of the shape $=$ Volume of part I+ Volume of part II

  $\Rightarrow$ Total volume of the shape $=2123.7{\text{ centimeter}}^3+5574.8{\text{ centimeter}}^3$

  $\Rightarrow$ Total volume of the shape $=7698.5{\text{ centimeter}}^3$

Conclusion:

Therefore, the total volume of the shape is $7698.5{\text{ centimeter}}^3.$