Chapter 12.5, Problem 27PPS

To determine

To determine the volume of each solid figure

Answer to Problem 27PPS

  $742.6{\text{ meter}}^3$

  $2448{\text{ meter}}^3$

  $3190.6{\text{ meter}}^3$

Explanation of Solution

Given:

  

Formula used:

Volume of the pyramid $=\frac{lwh}{3}\left[l=\text{length, }w\text{=}\text{width, }h\text{=}\text{height}\right]$

Volume of cuboid $=lwh\left[l=\text{length, }w\text{=}\text{width, }h\text{=}\text{height}\right]$

Calculation:

The given figure,

  

Splitting the image in two parts,

  

Taking part I:

  

Height of the pyramid $=9.1$ meter

Length of the base of the pyramid $=20.4$ meter

Width of the base of the pyramid $=12$ meter

Now, volume of the pyramid,

  $\Rightarrow$ Volume of the pyramid $=\frac{lwh}{3}$

  $\Rightarrow$ Volume of the pyramid $=\frac{9.1\times 12\times 20.4}{3}$

  $\Rightarrow$ Volume of the pyramid $=\frac{2227.68}{3}$

  $\Rightarrow$ Volume of the pyramid $=742.56{\text{ meter}}^3$

Rounding off to nearest tenth,

  $\Rightarrow$ Volume of the pyramid $=742.6{\text{ meter}}^3$

Taking part II:

  

Length of the cuboid $=20.4$ meter

Width of the cuboid $=12$ meter

Height of the cuboid $=10$ meters

Now, volume of the cuboid,

  $\Rightarrow$ Volume of the cuboid $=lwh\left[l=\text{length, }w\text{=width, }h\text{=height}\right]$

  $\Rightarrow$ Volume of the cuboid $=20.4\times 12\times 10$$\left[\because \text{Volume of the cuboid}=lwh\right]$

  $\Rightarrow$ Volume of the cuboid $=2448{\text{ meter}}^3$

Rounding off to nearest tenth,

  $\Rightarrow$ Volume of the cuboid $=2448{\text{ meter}}^3$

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

  $\Rightarrow$ Total volume of the shape $=742.6{\text{ meter}}^3+2448{\text{ meter}}^3$

  $\Rightarrow$ Total volume of the shape $=3190.6{\text{ meter}}^3$

Conclusion:

Therefore, the total volume of the shape is $3190.6{\text{ meter}}^3.$