Volume of 3D Object
Presentation
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Mathematics
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8th - 10th Grade
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Hard
Joseph Anderson
FREE Resource
26 Slides • 7 Questions
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volume of 3d objects
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How much liquid could these 3d object hold?
The volume is how we find out the answer to this question.
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For most 3d objects, the volume is found by finding the area of the base and multiplying that by the height.
Some exceptions are pyramids, cones, and spheres.
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We will use this as the base of a cylinder.
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area of the green circle was A=πr2
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Notice the area of a circle is in the formula for volume of a cylinder
we take the area of a circle and multiply it by the height of the cylinder to get the volume
a=πr2 and v=πr2h
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What information would we need to find the volume of this cylinder?
The radius is 8 and the height is 15.
We can use that info to substitute those values into our formula.
V=πr2H
V=π*82*15
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Multiple Choice
What is the volume(πr2h) of a cylinder with radius 3 and height 10?
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Notice the volume of a cone is almost the same as a cylinder. But a cone converges to a point(called a vertex).
We use the same formula for volume as the cylinder but we multiply by 1/3 or divide by 3(same thing) to find the volume of a cone.
V=(π*r2*h) /3
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Multiple Choice
What is the volume[(π*r2*H)/3] of a cone with radius 3 and height 7?
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spheres have a radius just like circles
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Notice the formula has a fraction bigger than 1 and the radius has an exponent of 3 now.
V=(4*π*r3) / 3
The radius of a sphere is from the center of the sphere to a point on the outside of the sphere.
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What information would we need to find the volume of this sphere?
The radius is 6. That is all we need to substitute for R in our formula.
V=(4*π*r3) / 3
V=4*π*63 / 3
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Multiple Choice
What is the volume[(4*π*r3)/3] of a sphere with radius 3?
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remember a square is a rectangle
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area of this base is L*W
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Notice the area of a rectangle is in the formula for volume of a rectangular prism
we take the area of a rectangle and multiply it by the height of the prism to get the volume
a=L*W and v=L*W*H
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What information would we need to find the volume of this rectangular prism?
Width=4 Length=4 Height=6
We can use that info to substitute those values into our formula.
V=W*L*H
V=4*4*6
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Multiple Choice
What is the volume(L*W*H) of this rectangular prism with width 2 and length 7 and height 4?
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we will use this as the base of a triangular prism.
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area of the triangle is (b*h) / 2
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Notice the area of a triangle is in the formula for volume of a triangular prism
we take the area of a triangle and multiply it by the length of the prism to get the volume
a=(B*H)/2 and v=(L*B*H) / 2
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What information would we need to find the volume of this triangular prism?
Length=15 Height=11 base=13
We can use that info to substitute those values into our formula.
V=(L*B*H) / 2
V=(11*13*15) / 2
Hint: you can divide by 2 early to make bigger numbers smaller if you do not have a calculator.
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Multiple Choice
What is the volume[(B*H*L)/2)] of a triangular prism with base 3 and height 6 and length 8?
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Notice the volume of a pyramid is almost the same as a prism. The base of the pyramid determines its name, just like with prisms.
The B is this formula stands for area of the base.
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We use the same formula for volume as the prism but we multiply by 1/3 or divide by 3(same thing) due to the object converging at a single vertex.
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Volume of a rectangular pyramid
V=(L*W*H) / 3
Volume of a triangular pyramid
a triangular pyramid volume formula can be simplified to
(B*H*L) / 6
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Multiple Choice
What is the volume[(L*W*H)/3] of a rectangular pyramid with width 8 and length 10 and height 6?
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Multiple Choice
What is the volume[(B*H*L) /6] of a triangular pyramid with base 3 and height 4 and length 4?
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You should now be able to find the volume of all these 3d objects.
Did you get all the quiz questions right?
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