Unit 1, Lesson 10
Volume
Integrated Math 3
10.1
Activity
Here are some solids. Find the area of each base.
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Here are some volume formulas:
A farmer wants to know the sizes of the inside of her barn and silo. Here is the information she has:
We can find the volume of a figure composed of three-dimensional solids by decomposing it into separate familiar shapes, finding the volume of each shape, and adding those volumes together.
For example, consider the composite figure shown. To calculate its volume, we start by decomposing it into a hemisphere and a cone. Then we find the volume of each shape.
We can find the volume of the cone using the formula . The cone’s radius measures 3 units, and its height measures 9 units, so its volume is cubic units because .
We can find the volume of a sphere using the formula . To find the volume of a hemisphere, we take half the volume of a sphere, which is . The volume of this hemisphere is cubic units because .
Lastly, we add the volume of the cone and hemisphere to get the volume of the solid: cubic units, because .