Week 26: Volume of Cones

Week 26: Volume of Cylinders, Cones, and

Spheres (round stuff!)...TODAY IS CONES!

Multiple Choice

What does volume measure?

• The amount of space within a perimeter.

• The amount of space taken up by a 3D object.

Multiple Choice

Is the red line a radius or diameter of the circle?

• Radius
• Diameter

Multiple Choice

Which label would NOT be appropriate for volume?

• $$ft^2$$

• $$cm^3$$

• $$ft^3$$

• $$in^3$$

Today, we are doing VOLUME OF CONES together! We will also cover Volume of Spheres to help you with your Wednesday Wayground)

HEY! WHY ARE THERE FRACTIONS IN MY FORMULAS??

This video shows the very cool RELATIONSHIP (no math! Just observing!) between the volume of a cone, a sphere, and a cylinder. What do you notice?

Word Cloud

LET'S MAKE A WORD CLOUD!

In just one or two words, what did you notice about the volume when he poured the blue liquid back and forth between cone/sphere/cylinder?

Now let's learn about finding the VOLUME of a CONE (yep, that also involves "pi" π)

Quick INTRO to CONES & SPHERES

Calculating Volume of a CONE

Multiple Choice

V = $$\frac{r^2\pi h}{3}$$

Mr. Hoffman is ordering a blue-raspberry shaved ice.

It comes in a 7 inch high cone with a 3 inch radius, as shown. 

Which is the closest estimate to the volume of Mr. Hoffman's shaved ice cup?

(Bonus: will Mr. Hoffman's tongue turn blue?)

• 21 cubic inches

  (and his tongue is definitely turning blue)

• 63 cubic inches

  (and his tongue is definitely turning blue)

• 66 cubic inches

  (and his tongue is definitely turning blue)

• 198 cubic inches

  (and his tongue is definitely turning blue)

Multiple Choice

V = $$\frac{r^2\pi h}{3}$$

What is the volume of the cone on the left?

Leave your answer "in terms of π "

(yep, that's an EXACT answer, mathematically!)

• 263.8π in³

• 791.3π in³

• 784π in³

• 28,224π in³

Multiple Select

V = $$\frac{r^2\pi h}{3}$$

Did you notice that the HEIGHT and the RADIUS used DIFFERENT UNITS OF MEASURE in the last problem (yards vs. inches)?

• I'm just now noticing that...

• I did see that!

• I saw that, but I'm not sure if I converted correctly?

Math Response

V = $$\frac{r^2\pi h}{3}$$

Second chance! Time to use your "pi" key on your calculator!

What is the volume of this same cone IN CUBIC INCHES rounded to the nearest tenth?

Type answer here

Correct Answer: 88668.3

Deg^°

Rad

​Time to review what you've learned so far
(Week 25 and Week 26)

Multiple Choice

What does the "B" in the volume formula V = Bh stand for?

• Bottom of the object
• Box
• Between
• Area of the base

Multiple Choice

What is the formula for AREA of a CIRCLE?

• $$A\ =\ \pi r^2$$

• $$A\ =\ \pi d$$

• $$A\ =\ 2\pi r$$

• $$A\ =\ bh$$

Multiple Choice

A beaker (like a clear measuring cup in your kitchen) is used to measure_____

• length

• volume

• mass

Multiple Choice

Find the volume of this cylinder. Round your answer to the nearest tenth.

Hint: use your π "pi" button on your calculator!

• 128.6 units³
• 1,286.1 units³
• 401.9 units³
• 5,144.6 units³

Match

Match the following formula to the shape

• CONE

• SPHERE

• CYLINDER

• CIRCLE

• $$V=\frac{\pi r^2h}{3}$$

• $$V=\frac{4\pi r^3}{3}$$

• $$V=\pi r^2h$$

• $$A\ =\ \pi r^2$$