Question

Find the volume of the composite solid. Round your answer to the nearest hundredth,5.1 m5.1 mThe volume is about cubic meters,

Answer 1

The figure shows a cube with a cone shape extracted from it.

Thus, to get the volume of the composite solid, we need to subtract the volume of the cone from the volume of the cube.

i.e. Volume of Solid = Volume of Cube - Volume of Cone

`\begin{gathered} \text{Volume of cube=}l* l* l=l^3 \\ l=5.1m\text{ (according to the question)} \end{gathered}`

Therefore the volume of the cube is:

`\text{Volume of cube = 5.1}^3=132.651m^3`

Now we need to get the volume of the cone:

The formula of the volume of a cone is:

`\begin{gathered} \text{Volume of cone = }(1)/(3)*\pi* r^2* h \\ \\ r=\text{radius of cone} \\ h=\text{height of cone} \end{gathered}`

The radius of the cone is the same as half the length of one edge of the cube

While the height of the cone is the same as the height of the cube.

A sketch is shown below:

Thus, height (h) of cone = 5.1m

radius (r) of cone = 2.55m

`\text{Volume of cone=}(1)/(3)*\pi*2.55^2*5.1=34.728m^3`

Thus, we can now find the volume of the composite solid as:

`\begin{gathered} \text{Volume of Composite Solid=} \\ 132.651m^3-34.728m^3 \\ \\ \therefore\text{Volume of Composite Solid=}97.923m^3\approx97.92m^3\text{ (To nearest Hundredth)} \end{gathered}`

The volume is: 97.92 cubic meters