8.7 Volume of Composite Shapes
Up to this point we have been dealing with a single shape at a time. However, there are many times when
we have more than one shape we need to find the volume of. For example, a typical house is a rectangular prism
with a triangular prism on top. To install a medical grade air filter in a house, you must know the volume of the
house. We can do this by finding the volume of the rectangular prism and adding it to the volume of the triangular
prism. This is a simple example of finding the volume of composite shapes with prisms, but now we will move on
to composite shapes with rounded objects.
Two Shapes Put Together
Imagine a grain silo, the place where farmers store their grain after a harvest. They are usually a cylinder
with a cone roof, and the grain is dropped into the silo at the very top of the cone. To know how much room farmers
have for storing their harvest, they must calculate the volume of the grain silo. To do this, simply find the volume
of the cylinder, find the volume of the cone, and add the two together. Let’s assume the radius of the silo is 10 N>,
the height of the cylinder part is 30 N>, and the height of the cone part is 10 N>.
Cone
10 N>
30 N>
10 N>
Ì = Çy ℎ
Ì ≈ ∗ 3.14 ∗ 10 ∗ 10
Ì ≈ 1046.67 N> Cylinder
Ì = Çy ℎ
Ì ≈ 3.14 ∗ 10 ∗ 10
Ì ≈ 3140 N> Total volume is: Ì ≈ 1046.67 . 3140 ≈ 4186.67 N> Regardless of what shapes we put together, or how many, we can always find the total volume by finding
the volume of parts and adding them together.
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Lesson 8.7
Answer the following questions using Í U {. r² and rounding your answer to the nearest hundredth where
necessary.
1. Find the volume of a pencil with a radius of 0.5 0, a cone height of 3 0, and a cylinder
height of 14 0.
2. Find the volume of a model rocket with a radius of 1 E, a cone height of 3 E, and a cylinder
height of 8 E.
Visual for
questions
1-6
3. Find the volume of a caulking gun with a radius of 2 0, a cone height of 3 0, and a cylinder height of
20 0.
4. Find the volume of a crayon with a radius of 2 , a cone height of 21 , and a cylinder height of
80 .
5. Find the volume of a model jet with a radius of 1 N>, a cone height of 3 N>, and a cylinder height of 6 N>.
6. Find the volume of a pencil with a volume of 110Ç , a cone height of 3 , and a cylinder height of
10 .
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œ
7. Find the volume of a propane gas tank with half spheres on either end that
has a radius of 3 N> and a length œ of 7 N>. (Note: The cylinder length does
not include the radius length.)
Visual for
questions
7-8
8. Find the volume of a submarine with half spheres on either end that has a radius of 6 and a cylinder
length œ of 15 . (Note: The cylinder length does not include the radius length.)
9. Find the volume of a grain silo with a half sphere on one end that has a diameter of
6 and a cylinder height (ℎ) of 15 . (Note: The cylinder height does not include the
radius length.)
Visual for
questions
9-10
š
10. Find the volume of a grain silo with a half sphere on one end that has a diameter of 6 N> and a cylinder
height (ℎ) of 35 N>. (Note: The cylinder height does not include the radius length.)
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