Mathematics: Find the volume of the composite solid

answer: 13750 pounds of sand to fill sandbags.step-by-step explanation:...

Find the volume of the composite solid

anikalee

11.03.2022

$V_{total}=293.50 cm^{3}$

Step-by-step explanation:

The composite solid is formed by a pyramid and a prism.

The formula of a pyramid is

$V_{pyramid}=\frac{1}{3}Bh$

The formula of a rectangular prism is

$V_{prism}=l\times w\times h$ .

The total volume is

$V_{total}=V_{pyramid} +V_{prism}$

Where,

$B=6.7cm\times 6.2 cm=41.51 cm^{2}$

$V_{prism}=l\times w\times h=6.7cm \times 6.2cm \times 5.5cm=228.47cm^{3}$

Now, we need to find the height of the pyramid using the pythagorean theorem

$5.8^{2}=(\frac{6.7}{2} )^{2}+h^{2} \\33.64=11.22+h^{2}\\h^{2} =33.64-11.22=22.42\\h=\sqrt{22.42} \approx 4.7$

So, the volume of the pyramid is

$V_{pyramid}=\frac{1}{3}Bh=\frac{1}{3}(41.51)(4.7)=65.03cm^{3}$

Therefore, the volume of the composite figure is

$V_{total}=65.03cm^{3}+228.47cm^{3}=293.50 cm^{3}$

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