Question

Select the appropriate shape for the given volume formula,Rectangular prismCylinder Cone Sphere

Answer 1

`\begin{gathered} V_{\text{cylin}}=\pi r^2\text{ h}\rightarrow\text{cylinder} \\ V=(4)/(3)\text{ }\pi r^3\rightarrow sphere \\ V=\text{ lwh}\rightarrow rec\tan gular\text{ prism} \\ V=(1)/(3)\text{ }\pi r^2\text{ h}\rightarrow cone \end{gathered}`

Step-by-step explanation

Step 1

the volume of a cylinder is given by:

`V_{\text{cyli}}=\pi r^2\text{ h}`

so,

`V_{\text{cylin}}=\pi r^2\text{ h}\rightarrow\text{cylinder}`

Step 2

the volume of a sphere is given by:

`V=(4)/(3)\text{ }\pi r^3`

hence

`V=(4)/(3)\text{ }\pi r^3\rightarrow sphere`

Step 3

the volume of a rectanglular prism is given by

`\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}`

Step 4

the volume of a cone is given by:

`V=(1)/(3)\text{ }\pi r^2\text{ h}`

threfore

`V=(1)/(3)\text{ }\pi r^2\text{ h}\rightarrow cone`

I hope this helps you