Question

Find the volume of the composite solid

Answer 1

Explanation:

Find the volume of the composite solid. The solid is made up of a square prism and a square pyramid. Find each volume. ...

Find the volume of the composite solid. Round your answer to the nearest tenth. ...

What is the volume of the silver ring in an Argentine peso? Round your answer to the nearest tenth

Answer 2

`V_(total)=293.50 cm^(3)`

Explanation:

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

The formula of a pyramid is

`V_(pyramid)=(1)/(3)Bh`

The formula of a rectangular prism is

`V_(prism)=l* w* h`.

The total volume is

`V_(total)=V_(pyramid) +V_(prism)`

Where,

`B=6.7cm* 6.2 cm=41.51 cm^(2)`

`V_(prism)=l* w* h=6.7cm * 6.2cm * 5.5cm=228.47cm^(3)`

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

`5.8^(2)=((6.7)/(2) )^(2)+h^(2) \\33.64=11.22+h^(2)\\h^(2) =33.64-11.22=22.42\\h=√(22.42) \approx 4.7`

So, the volume of the pyramid is

`V_(pyramid)=(1)/(3)Bh=(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)`