Math Rocks!

𝑉 =1

3𝐵ℎ

All polygons have straight sides.

Pyramid – A solid object where the base is a polygon and the sides are triangles which meet at the top

The apex is highest point.

10 m

10 m

Apex

Base

Pyramids are identified by type of base they have.

This would be a square pyramid.

10 m

10 m

The dashed lines will indicate lines hidden by a solid polygon.

Draw lines from the four vertices to an

apex above the rhombus.

10 m

10 m

Why must you use the Pythagorean theorem?

To find the height of the pyramid.

Solve for volume

𝑉 =1

3𝐵ℎ

𝑎2 + 52 = 132

𝑎2 + 25 = 169

𝑎2 = 144

𝑎 = 12

ℎ = ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑝𝑦𝑟𝑎𝑚𝑖𝑑ℎ = 12 𝑚

13 m

𝐵 = 10 𝑚 ∙ 10 𝑚 = 100 𝑚2𝐵 = 𝐴𝑟𝑒𝑎 𝑜𝑓 𝐵𝑎𝑠𝑒

10 m

10 m

How do we proceed?

Just substitute and solve.

13 m

12 m

𝑉 =1

3100 𝑚2 12 𝑚

𝑉 =1

31200 𝑚3

𝑉 = 400 𝑚3

𝑉 =1

3𝐵ℎ

ℎ = 12 𝑚

𝐵 = 100 𝑚2

h=481 ft.s=756 ft.

h=heights=side of baseB= side squared

What must you do after substituting

the values? Follow the order of operations.

𝑉 =1

3571,536 𝑓𝑡2 481 𝑓𝑡

𝑉 =1

3756 𝑓𝑡 2 ∙ 481 𝑓𝑡

𝑉 =1

3274,908,816 𝑓𝑡3

𝑉 = 91,636,272 𝑓𝑡3

h=24 ms=55 m

h=heights=side of baseB= side squared

Why do mummies tell no secrets?

𝑉 =1

33,025 𝑚2 24 𝑚

𝑉 =1

355 𝑚 2 ∙ 24 𝑚

𝑉 =1

372,600 𝑚3

𝑉 = 24,200 𝑚3

Because they keep things under wraps.

h=72 ft.s=112 ft.

h=heights=side of baseB= side squared

Why might you want to know the volume

of the Louvre.

𝑉 =1

312,544 𝑓𝑡.2 72 𝑓𝑡.

𝑉 =1

3112 𝑓𝑡. 2 ∙ 72 𝑓𝑡.

𝑉 =1

3903,168 𝑓𝑡.3

𝑉 = 301, 056 𝑓𝑡.3

For heating and cooling purposes.

h=65 ms=225 m

h=heights=side of baseB= side squared

Who belongs to the Pyramid

PTA?

𝑉 =1

350,625 𝑚2 65 𝑚

𝑉 =1

3225 𝑚 2 ∙ 65 𝑚

𝑉 =1

33,290,625 𝑚3

𝑉 = 1,096,875 𝑚3

Mummies and Deadies!

For this problem you are not give the side of

the square base, but the perimeter.

Divide the perimeter by four.

𝑃 =2,600 𝑓𝑡

4

𝑃 = 650 𝑓𝑡.

h=350 ft.s=650 ft.

h=heights=side of baseB= side squared

Why couldn’t the mummy answer the

phone?

𝑉 =1

3422,500 𝑓𝑡.2 350 𝑓𝑡.

𝑉 =1

3650 𝑓𝑡. 2 ∙ 350 𝑓𝑡.

𝑉 =1

3147,875,000 𝑓𝑡.3

𝑉 = 49,291,667𝑓𝑡.3

She was tied up!

Review Questions

What information is not needed to find the volume?

The height of the triangle face.

What do you call the top of a pyramid?

Apex

Of corpse!Do mummies enjoy being mummies.

When give the perimeter of the base, how do you find the side of the base?

Divide the perimeter by four.

Review Questions

How do you identify a pyramid?

By the type of base.

What would you call a pyramid in which all the sides of the base are congruent with right angles?

A square pyramid

If you did not want multiply by one-third

what else could you do?

Divide by 3 1

3𝐵ℎ =

𝐵ℎ

3

If you are not a Math Monkey then you are a chimp.

Copyright © 2013 Daryle Fleming

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