[tex]\begin{gathered} V_{\text{cylin}}=\pi r^2\text{ h}\rightarrow\text{cylinder} \\ V=\frac{4}{3}\text{ }\pi r^3\rightarrow sphere \\ V=\text{ lwh}\rightarrow rec\tan gular\text{ prism} \\ V=\frac{1}{3}\text{ }\pi r^2\text{ h}\rightarrow cone \end{gathered}[/tex]
Explanation
Step 1
the volume of a cylinder is given by:
[tex]V_{\text{cyli}}=\pi r^2\text{ h}[/tex]
so,
[tex]V_{\text{cylin}}=\pi r^2\text{ h}\rightarrow\text{cylinder}[/tex]
Step 2
the volume of a sphere is given by:
[tex]V=\frac{4}{3}\text{ }\pi r^3[/tex]
hence
[tex]V=\frac{4}{3}\text{ }\pi r^3\rightarrow sphere[/tex]
Step 3
the volume of a rectanglular prism is given by
[tex]\begin{gathered} \text{Volume}=\text{length}\cdot\text{width}\cdot\text{height} \\ V=\text{ lwh} \\ \text{hence} \\ V=\text{ lwh}\rightarrow rec\tan gular\text{ prism} \end{gathered}[/tex]
Step 4
the volume of a cone is given by:
[tex]V=\frac{1}{3}\text{ }\pi r^2\text{ h}[/tex]
threfore
[tex]V=\frac{1}{3}\text{ }\pi r^2\text{ h}\rightarrow cone[/tex]
I hope this helps you
