Volumes of Cones/Pyramids (2 days)

Volumes of Cones/Pyramids

Learning outcome:

By the end of this lesson, students will be able to accurately apply the formulas for the volumes of pyramids and cones to calculate the volume of these shapes in various contexts, demonstrating their understanding through solving both theoretical problems and practical examples.

Last class we said the volume of a prism is the area of its base times its height.

​Volume = area of the base x height of prism

​​Prisms: V = Bh

​

​Note: Because you are multiplying all 3 dimensions together, the units will be cubed.

Approximate Volume

Multiple Choice

^{_{Estimate the volume.}}

• 163in³

• 18in³

• 283in³

• 324in³

Multiple Choice

What is the volume of the rectangular prism?

• 40 square inches

• 120 square inches

• 120 cubic inches

• 158 square inches

• 158 cubic inches

Fill in the Blanks

Multiple Choice

What is the volume of the triangular prism?

• 90 cm cubed

• 98.5 cm cubed

• 180 cm cubed

Multiple Choice

What shape is this?

• Cone

• Sphere

• Cube

• Pyramid

Multiple Choice

How do you find the volume of a cone?

• V= ^1/₃ πr²h

• V= ^4/₃ πr²h

• V= ^4/₃ πr³

• V= πr²h

Cones

Multiple Choice

Find the Volume of the Cone

• 150.72 cm³

• 75.36 cm³

• 452.16 cm³

• 155 cm³

Multiple Choice

Find the volume of the following cone.

• 602.9

• 60.3

• 1808.6

• 180.9

Multiple Choice

Which label would NOT be appropriate for volume.

• square miles

• inches³

• cm³

• cubic feet

Open Ended

Avery was given this cone and asked to find the volume. The following is the set up of her equation: $$v=\frac{1}{3}\pi\left(18\right)^2\left(18\right)$$ . What did she do incorrectly?

Volume of Pyramids

17

It’s concluded. The formula for the volume of a rectangular
pyramid is below.The animation shows again the relationship.

B = base area

h = height of the figure

V = Bh

1
3

​

• ​2 parallel and congruent bases

• surrounding faces are rectangles

​​Prisms:

​

​

• 1 base

• surrounding faces are triangles​

​​Pyramids:

​

Multiple Choice

What is the shape of the base?

• Rectangle

• Triangle

• Circle

• Trapezoid

Multiple Choice

What is the formula for area of a rectangle?

• A=3.14r^2

• A=1/2bh

• A=lw

• A=1/2(b1+b2)h

Multiple Choice

What is the height of the pyramid?

• 10cm

• 6cm

• 11cm

Multiple Choice

What is the volume of rectangular pyramid?

• 660 cm^3

• 220 cm^3

• 330 cm^3

• 110 cm^3

Steps to solving Volume of Pyramid

1. Determine the Area of the base

2. Multiply by the height

3. Divide by 3.

Match

Match the formula to the correct shape.

• Volume of Pyramids

• Area of Triangles

• Volume of Prisms

• Area of Rectangle or Square

V= 1/3Bh

A= 1/2bh

V= Bh

A= bh

• V= 1/3Bh

• A= 1/2bh

• V= Bh

• A= bh

Multiple Choice

What is the shape of the base?

• Square

• Circle

• Triangle

• Hexagon

Multiple Choice

What is the formula for the area of the base?

• bh

• 1/3bh

• 1/2bh

• 1/2(b1+b2)h

Multiple Choice

What is the height of the pyramid?

• 4

• 3

• 5

• 6

Multiple Choice

What is the volume of the triangular pyramid?

• 6 mm^3

• 36 mm^3

• 18 mm^3

• 12 mm^3

Multiple Choice

What is the approximate volume of the right triangular pyramid?

• 952 units cubed

• 317 units cubed

• 635 units cubed

• 1904 units cubed

Multiple Choice

What is the volume of the triangular pyramid?

• 576 units^3

• 96 units^3

• 288 units^3

• 192 units^3

Multiple Choice

What is the volume of the pyramid?

• 168m³

• 84m³

• 56m³

• 174m³

Multiple Choice

Solve for the volume of the rectangular pyramid

• 360 ft^3

• 1080 ft^3

• 180 ft^

• 216 ft^3

Multiple Choice

What is the volume of the triangular pyramid?

• 150 cm^3

• 75 cm^3

• 25 cm^3

• 50 cm^3

Multiple Choice

Solve for the volume of the rectangular pyramid

• 192 cm^3

• 576 cm^3

• 288 cm^3

• 96 cm^3

Multiple Choice

What is the volume of the triangular pyramid?

• 576 units^3

• 96 units^3

• 288 units^3

• 192 units^3

Fill in the Blanks