SECTION 9.2VOLUME OF PRISMS
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I) REVIEW: PRISMS
Prisms are 3D objects where two opposite sides areparallel and have the same shape
A rectangular Prism is a prism where the opposite endsare rectangles/squares
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Triangular Prism
Pentagonal Prism
Hexagonal Prism
REVIEW: AREA OF A TRIANGLE
The base and height of a triangle must always be perpendicular
The area of a triangle is given by the equation:
Ex: Find the area of each of the following triangles
Use the Pyth. Thm.to find the height
Now get the area usingthe height
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VOLUME OF A PRISMS
When finding the volume of a prism, get the area of thebase and then multiply with the height
If the prism is a cube or a rectangular prism, just multiplythe length, width and height together
If the shape is a triangular prism, get the area of thetriangle and then multiply it by the height
Note: height distance between the two triangles
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EX: FIND THE VOLUME OF EACH SOLID:
The base of this prism is a triangle
The area of a triangle is:
Multiply the base by the distancebetween the two triangles for thevolume
The base is a triangle
The area of a triangle is:
Multiply the base by the distancebetween the two triangles for thevolume
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Ex: John wants to heat his home by filling it with hot air.Given the dimensions of the house, what is the volume in m3?
The house is in the shape of apentagonal prism
Find the area of the base (pentagon)
Get the volume by using the base
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Ex: Cindy has a large fish tank with dimensions: 2m x32cm x 55cm. If the tank is ¾ full with water, howmuch more water does she need to add until it is 100%full? Give your answer in millimeters.
The tank is ¾ full, that means it needs ¼ of the
tank’s volume to fill it up
Divide the volume by 4 to find out what you need to add
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EX: A WATER TANK HAS DIMENSIONS (L)80CM BY(D)40CM BY (H)50CM. THE WATER IN THE TANK IS 80%FULL. A SOLID CUBE WITH DIMENSIONS 20CM BY 20CMBY 20CM IS DUMPED INTO THE TANK. HOW MANY CMDOES THE WATER LEVEL INCREASE BY?
Since the tank was 80% full, the height ofthe water before the cube was 80% of 50cm
The volume of the cube and water is:
Now get the height of the waterafter the cube was added:
The height increased by 2.5cm
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HOMEWORK:
P259 #6 – 10, 13, 16, 19, and 24
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