Volume of irregular shapes
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The house below is made of two 3-d 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 feet3
volume of rectangular prism = 15 × 15 × 50 = 11250 feet3
Volume of house = 3750 + 11250 = 15000 feet3
A couple more great examples showing how to calculate the volume of irregular shapes
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
Volume = volume of half the sphere + volume of the cone
Volume of a sphere =
4 × π × r3
3
Volume of a sphere =
42.39
3
Volume = 14.13 inches3
Since it is half a sphere, we get 7.065 inches3
Volume of a cone =
π × r2 × h
3
Volume of a cone =
3.14 × 1.52 × 6.5
3
Volume of a cone =
45.9225
3
Volume of cone = 15.3075 inches3
Volume of the whole thing is 7.065 + 15.3075 = 22.3725 inches3
A box containing 4 cream cones:
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 inches3
volume of a cone =
π × r2 × h
3
volume of a cone =
3.14 × 12 × 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 inches3
Hopefully you know now how to find the volume of irregular shapes!