Question

5. In the video the speaker explains a way to get the volume is to find the area of the base and then multiply by how the base has been extended, or the height. He gives you some examples and their formulas. State the formulas of the following 3 dimensional shapes with a brief definition of the shape: Ex. Cube: base of a square, with the height the same as the length of one side. If s = length of one side then Volume of a cube = s*s*s or S^3. a. Rectangular Prism = b. Triangular Prism = c. Cylinder = d. Sphere = e. Cone =

Answer 1

a) Rectangular prism

The volume of rectangular prism = base area x height

= W x L x H

b) Triangular prism

The volume of the triangular prism

`\begin{gathered} =\text{ Base area x Length} \\ =\text{ }(1)/(2)\text{ B x H x L} \end{gathered}`

c) Cylinder

The base area of a cylinder is the area of a circle.

The volume of a cylinder

`\begin{gathered} =\text{ Base area X height} \\ =\text{ }\pi r^2\text{ x h} \\ =\text{ }\pi r^2h \end{gathered}`

d) Sphere

`\text{The volume of a sphere = }(4)/(3)\text{ }\pi r^3`

e) Cone

The base area of a cone is the area of a circle.

The volume of a cone

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