12.4 Volume of Prisms & Cyl./12.5 Volume of Pyram. & Cones

​12.4 Volumes of Prisms and Cylinders/ 12.5 Volumes of Pyramids and Cones

"​Never stop learning because life never stops teaching"

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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.

Remember a square is a rectangle.

area of this base is L*W

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.

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

Drag and Drop

Which is the formula for the volume of a rectangular prism?

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#6

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Length x Width x Height

Base x Height

Length x Width

Surface Area x Height

Dropdown

What is the volume of the rectangular prism? #4

Select answer

Drag and Drop

What is the volume of this prism?

Placeholder

#5

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40 cubic feet

20 cubic feet

8 cubic feet

Multiple Choice

$$V=Bh\ wher\ B\ is\ the\ area\ of\ the\ triangle.\ B=\frac{\left(\left(base\right)height\right)}{2}$$  Find the volume of the figure. Round to the nearest tenth. #8

• 80 cm³

• 40 cm²

• 80 cm²

• 40 cm³

Multiple Choice

Find the volume of the figure. Round to the nearest whole number. #9

• 1,944 cm³

• 108 cm³

• 972 cm³

• 216 cm³

We will use this as the base of a cylinder.

The area of the green circle is A=πr².

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.

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

Multiple Choice

Find the volume of the cylinder. $$V=\pi r^2h\ where\ r\ is\ the\ radius\ and\ h\ is\ the\ height.$$  #1

• 4239

• 1696

• 1130

• 565

Dropdown

A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift. What is the approximate volume of the tube? Round to the nearest whole cubic centimeter.

Select answer

#7

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

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

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.

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

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

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

Multiple Choice

Find the height (h) of the cone. #36

• 5.0 m

• 5.3 m

• 5.7 m

• 6.0 m

Multiple Choice

Find the volume of the composite solid. $$V_{total}=V_{cone}+V_{cylinder}$$   $$V_{total}=\frac{\pi r^2h_{cone}^{ }}{3}+\pi r^2h_{cylinder}$$   Remember there are two different heights. #33

• 890.1 cm³

• 178.0 cm³

• 576.0 cm³

• 874.3 cm³

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

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

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