Volume of irregular shapes
You can calculate the volume of irregular shapes easily once you know how to get the volume of a single threedimensional shape .
A house
The house above is made of two 3d shapes: A triangular prism and a rectangular prism
The roof of the house is the one shaped like a triangular prism
Volume of house = volume of triangular prism + volume of rectangular prism
volume of triangular prism = area of triangle × length of house
volume of triangular prism =
base of triangle × height of triangle
/
2
× length of house
length of house = 50 feet, base of triangle = 15 feet, and height of triangle = 10 feet
volume of triangular prism =
15 × 10
/
2
× 50
volume of triangular prism = 75 × 50 = 3750 feet
^{3}
volume of rectangular prism = 15 × 15 × 50 = 11250 feet
^{3}
Volume of house = 3750 + 11250 = 15000 feet
^{3}
Ice cream cone:
When you order ice cream, you may have never realized that it could be a combination of half a sphere and a cone
Of course, we have to assume that the shape made by the ice cream scoop is half a sphere.
The shape of my ice cream shown below is half a sphere and then we put it on a cone. What is the volume?
It may be easier to see how to compute the volume if we remove the ice cream
Pretend that the radius of the cone or r is 1.5 inches and the height of the cone or h is 6.5 inches here is how to compute the volume
Volume = volume of half the sphere + volume of the cone
volume of a sphere =
4 × π × r^{3}
/
3
volume of a sphere =
42.39
/
3
volume = 14.13 inches
^{3}
Since it is half a sphere, we get 7.065 inches
^{3}
volume of a cone =
π × r^{2} × h
/
3
volume of a cone =
3.14 × 1.5^{2} × 6.5
/
3
volume of a cone =
45.9225
/
3
volume of cone = 15.3075 inches
^{3}
volume of the whole thing is 7.065 + 15.3075 = 22.3725 inches
^{3}
A box has 4 identical ice cream cones arranged inside of the box as shown below. The radius of the base of the cone is 1 inch and the height is 6 inches
What is the volume of the
space left inside the box ?
Space left inside the box = volume of box  volume of 4 cones
Volume of box = 8 × 8 × 8 = 512 inches
^{3}
volume of a cone =
π × r^{2} × h
/
3
volume of a cone =
3.14 × 1^{2} × 6
/
3
volume of a cone = 6.28. Therefore, volume of 4 cones = 4 × 6.28 = 25.12
Volume left inside = 512  25.12 = 486.88 inches
^{3}
Hopefully you know now how to find the volume of irregular shapes!

Mar 13, 19 11:50 AM
Learn how to derive the equation of an ellipse when the center of the ellipse is at the origin.
Read More
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.