Volume of Pyramids, Cones, and Spheres

Volume of Pyramids, Cones, and Spheres

You need out your reference sheet from last class! Ask for a new one if you lost it!

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

Multiple Choice

In the first video, they had to empty the cone into the cylinder three times to fill the cylinder. In the second video, they had to empty the pyramid into the prism three times to fill the prism.

Based on that, what should the formula for volume of cones and pyramids be?

• $$V=3Bh$$

• $$V=\frac{Bh}{3}$$

We have to divide by three!

Jot this down!

Multiple Choice

How do you find B for this cone?

• It is just 9.

• You take $$\pi\cdot9^2$$

• You do $$\frac{\left(9\cdot12\right)}{2}$$

• It is $$9\cdot12$$

Multiple Choice

The value of B is $$\pi\cdot9^2$$ . Now find the volume of the cone to the nearest tenth.

• 3053.6 cubic meters

• 36 cubic meters

• 113.1 cubic meters

• 1017.9 cubic meters

Multiple Choice

What is the radius of this cone?

• 16

• 17

• 8

• 33

Multiple Choice

What is the height of the cone that you will use when you find the volume.

(Notice that the 17cm is down the outside and not through the center like we want!)

• 8

• 16

• 15

• 17

Fill in the Blanks

Fill in the Blanks

Last but not least... Spheres!

Add to your notes!

How do I put this in my calculator?

​Find the volume of a sphere with r = 9.

Type in 4÷3×π×9^3.

The ^ key lets you put in any exponent.

You should get 3053.628059.

Multiple Choice

Try it!

Find the volume of the given sphere.

• 1,563.5 cubic in.

• 1,325.5 cubic in.

• 1,129.9 cubic in.

• 1,819.6 cubic in.

Multiple Choice

How would you find the volume of a shape like this?

• Look for a magical formula for a hemisphere/ cylinder hybrid.

• Find the volumes of the hemisphere and cylinder separately and then add them.

• Find the volumes of the hemisphere and cylinder separately and then subtract them.

Fill in the Blanks

Here is my work.

Cylinder: V = π×6²×9 = 1017.876

Hemisphere: 2÷3×π×6³ = 452.389

Total Volume = 1017.876 + 452.389

Total Volume = 1470.265

Time to Practice on your Own

Multiple Choice

The dimensions of grain storage bins in the shape of a cylinder and a rectangular prism are shown. Which measurement is closest to the difference between the volumes of the 2 bins?

• 24,280 cubic feet

• 16,430 cubic feet

• 11,720 cubic feet

• 4,480 cubic feet

Multiple Choice

Find the volume:

• 960 cm ³
• 240 cm ³
• 960 cm ²
• 1920 cm ³

Multiple Choice

Find the volume of the cone. (Round to the nearest integer.)

• 1810 in³

• 151 in³

• 452 in³

• 276 in

Multiple Choice

Find the volume of the figure.

• 1,800 cm³
• 900 cm³
• 600 cm³
• 750 cm³

Multiple Choice

Find the volume to the nearest hundredth using 3.14 instead of Pi.

• 5572.45 cm³

• 506.59 cm³

• 126.65 cm³

• 1393.11 cm³

What now?

You have a paper assignment due next class.

Complete the assignment. We will take a quiz over volume the second half of class next time. If you have questions, please come see Mrs. Cooper during Warrior Time or before or after school before then.

Reminder!

You had an assignment on google forms due today! Go back and do it if you haven't yet!