Question

Find the volumes of the three solids. What do you notice?

Answer 1

The volume of the solids are;

`\begin{gathered} \text{Hemisphere V}_1=2,094.4\text{ }m^3 \\ \text{Cylinder V}_2=3,141.6\text{ }m^3 \\ \text{Cone V}_3=1,047.2\text{ }m^3 \end{gathered}`

We can observe that ;

`\begin{gathered} V_2=3V_3 \\ V_1=2V_3 \end{gathered}`

The volume of the cylinder is three times the volume of the cone and the volume of the hemisphere is twice the volume of the cone.

Step-by-step explanation:

Given the three solids in the attached image.

We want to find the volume of each.

The hemisphere;

`\begin{gathered} V_1=(2)/(3)\pi r^3 \\ r=10m \end{gathered}`

Substituting the values;

`\begin{gathered} V_1=(2)/(3)\pi(10^3) \\ V_1=2,094.4m^3 \end{gathered}`

The cylinder;

`\begin{gathered} V_2=\pi r^2h \\ r=10m \\ h=10m \end{gathered}`

substituting the values

`\begin{gathered} V_2=\pi*10^2*10 \\ V_2=3000\pi \\ V_2=3,141.6m^3 \end{gathered}`

The cone;

`\begin{gathered} V_3=(1)/(3)\pi r^2h \\ r=10m \\ h=10m \end{gathered}`

substituting the values;

`\begin{gathered} V_3=(1)/(3)\pi*(10^2)*10 \\ V_3=1,047.2m^3 \end{gathered}`

Therefore, the volume of the solids are;

`\begin{gathered} \text{Hemisphere V}_1=2,094.4\text{ }m^3 \\ \text{Cylinder V}_2=3,141.6\text{ }m^3 \\ \text{Cone V}_3=1,047.2\text{ }m^3 \end{gathered}`

we can observe that ;

`\begin{gathered} V_2=3V_3 \\ V_1=2V_3 \end{gathered}`

The volume of the cylinder is three times the volume of the cone and the volume of the hemisphere is twice the volume of the cone.