12 pentagons make up this dodecahedron. Click here to see how to calculate the area of a pentagon.
|The dodecahedron is made up of 12 pyramids with pentagon as the base.|
The volume of one pyramid = (base area × height) /3 = 12 × the volume of pyramid.
To calculate the height of the pyramid, use the Pythagoras theorem,
height = √(R² - r²), where R is the radius of the dodecahedron and r is the radius of each pentagon.
V = 15 + [(7√5) / 4]a³