Answer to Question #193834 in Geometry for Melissa

Question

Explain how to calculate the volumes of the following shapes:

• a cuboid

• a sphere

• a cone

• a triangular prism

• a cylinder

Answer 1

Cuboid whose length = l, width = w and height = h

To find the volume of a cuboid, multiply its length by its width by its height. This can be written as: v o l u m e = l × w × h.

Sphere whose radius = $r$

Volume of sphere =$\dfrac{4}{3}\pi r^3$

Cone having height = $h$ , radius = $r$ and slant height = $l$

Volume of cone =$\dfrac{1}{3}\pi r^2h$

The general formula for calculating the volume of any prism is:

Volume = (Area of the base) $\times$ length

For a triangular prism, the formula would be:

Volume = (Area of the triangular base) $\times$ length 

Cylinder whose radius = $r$ , height = $h$

Volume of cylinder =$\pi r^2 h$