Respuesta :
Answer:
The volume of the solids are;
[tex]\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}[/tex]We can observe that ;
[tex]\begin{gathered} V_2=3V_3 \\ V_1=2V_3 \end{gathered}[/tex]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.
Explanation:
Given the three solids in the attached image.
We want to find the volume of each.
The hemisphere;
[tex]\begin{gathered} V_1=\frac{2}{3}\pi r^3 \\ r=10m \end{gathered}[/tex]Substituting the values;
[tex]\begin{gathered} V_1=\frac{2}{3}\pi(10^3) \\ V_1=2,094.4m^3 \end{gathered}[/tex]The cylinder;
[tex]\begin{gathered} V_2=\pi r^2h \\ r=10m \\ h=10m \end{gathered}[/tex]substituting the values
[tex]\begin{gathered} V_2=\pi\times10^2\times10 \\ V_2=3000\pi \\ V_2=3,141.6m^3 \end{gathered}[/tex]The cone;
[tex]\begin{gathered} V_3=\frac{1}{3}\pi r^2h \\ r=10m \\ h=10m \end{gathered}[/tex]substituting the values;
[tex]\begin{gathered} V_3=\frac{1}{3}\pi\times(10^2)\times10 \\ V_3=1,047.2m^3 \end{gathered}[/tex]Therefore, the volume of the solids are;
[tex]\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}[/tex]we can observe that ;
[tex]\begin{gathered} V_2=3V_3 \\ V_1=2V_3 \end{gathered}[/tex]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.
