
12.4 Volume of Prisms & Cyl./12.5 Volume of Pyram. & Cones
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Mathematics
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10th Grade
•
Easy
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Standards-aligned
Larry Cooper
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30 Slides • 19 Questions
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12.4 Volumes of Prisms and Cylinders/ 12.5 Volumes of Pyramids and Cones
"Never stop learning because life never stops teaching"
-Unknown
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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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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=4cm, Length=4cm, and Height=6cm
We can use that information to substitute those values into our formula.
V=W*L*H = 4*4*6= 96cm3
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Drag and Drop
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Dropdown
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Drag and Drop
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Multiple Choice
V=Bh wher B is the area of the triangle. B=2((base)height) Find the volume of the figure. Round to the nearest tenth. #8
80 cm³
40 cm²
80 cm2
40 cm³
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Multiple Choice
Find the volume of the figure. Round to the nearest whole number. #9
1,944 cm³
108 cm³
972 cm³
216 cm³
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We will use this as the base of a cylinder.
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The area of the green circle is A=πr2.
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Notice the area of a circle is in the formula for the 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
Find the volume of the cylinder. V=πr2h where r is the radius and h is the height. #1
4239
1696
1130
565
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Dropdown
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Multiple Choice
A square-based prism has a cylindrical hole bored through the middle as shown in the diagram above.
What is the approximate remaining volume of the prism? Use 3.14 for π. #16
a. 226.08 cubic centimeters
b. 247.68 cubic centimeters
c. 925.92 cubic centimeters
d. 1,052 cubic centimeters
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Multiple Choice
The four diagonals of a cube are drawn to create 6 square pyramids with the same base and height. The volume of the cube is (b)(b)(b). The height of each pyramid is h.
Therefore, the volume of one pyramid must equal one-sixth the volume of the cube, or #43
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Multiple Choice
What is the formula for the VOLUME of a PYRAMID? #40
V=1/2pl
V=4/3(pi)r3
V=1/3Bh
V=1/3(pi)r2h
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Multiple Choice
A right square pyramid has a height of 15 cm. and a slant height of 25 cm.
What is the volume of the pyramid? #41
2400 cubic cm.
6000 cubic cm.
8000 cubic cm.
24000 cubic cm.
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Multiple Choice
Helen has 48 cubic inches of clay to make a solid square right pyramid with a base edge measuring 6 inches.
Which is the slant height of the pyramid if Helen uses all the clay? #43
3 inches
4 inches
5 inches
6 inches
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Multiple Choice
What is the volume of the composite figure? #45
140 cubic inches
147 cubic inches
168 cubic inches
196 cubic inches
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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
v = ?
***Remember to take half of the diameter to get the radius.***#31
2,144.66 m3
1,608.49 m3
536.17 m3
498.62 m3
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Multiple Choice
Find the height (h) of the cone. #36
5.0 m
5.3 m
5.7 m
6.0 m
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Multiple Choice
Find the volume of the composite solid. Vtotal=Vcone+Vcylinder Vtotal=3πr2hcone+πr2hcylinder Remember there are two different heights. #33
890.1 cm3
178.0 cm3
576.0 cm3
874.3 cm3
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Multiple Choice
The volume of a rectangular prism changes from 1,250 cubic inches to 125 cubic inches. What is the scale factor of the change? #27
1/2
1/10
10
1/5
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Multiple Choice
The volume of the cylinder is dilated by a scale factor of 3, what is the volume of the new cylinder in ft³? #25
162 ft³
180 ft³
54 ft³
108 ft³
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Multiple Choice
The two square pyramids are similar. Find the volume of the red pyramid. #28
12 in3
21.3 ft3
16 ft3
6.75 in3
12.4 Volumes of Prisms and Cylinders/ 12.5 Volumes of Pyramids and Cones
"Never stop learning because life never stops teaching"
-Unknown
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