Lesson 23

​

estimating a hemisphere

Warm Up

Lesson

Summary

Cool

Down

Reflections

Student

Task

Learning

Targets

Practice Problems

Lesson Video

Unit 6

functions and volume

SLIDESMANIA.COM

23.1 Warm Up - Notice and Wonder: Two Shapes

Here are two shapes.

​

​

​

​

​

​

​

​

​

​

What do you notice? What do you wonder?

SLIDESMANIA.COM

Learning Targets

• I can estimate the volume of a hemisphere by calculating the volume of shape I know is larger and the volume of a shape I know is smaller.

Success Criteria

Today I am using the volume of a sphere to find the volume of a hemisphere.

SLIDESMANIA.COM

23.2 Hemispheres in Boxes

1. Mai has a dome paperweight that she can use as a magnifier. The paperweight is shaped like a hemisphere made of solid glass, so she wants to design a box to keep it in so it won't get broken. Her paperweight has a radius of 3 cm.
1. What should the dimensions of the inside of box be so the box is as small as possible?
2. What is the volume of the box?
3. What is a reasonable estimate for the volume of the paperweight?

SLIDESMANIA.COM

23.2 Hemispheres in Boxes

• Tyler has a different box with side lengths that are twice as long as the sides of Mai's box. Tyler's box is just large enough to hold a different glass paperweight.
• What is the volume of the new box?
• What is a reasonable estimate for the volume of this glass paperweight?
• How many times bigger do you think the volume of the paperweight in this box is than the volume of Mai's paperweight? Explain your thinking

SLIDESMANIA.COM

23.3 Estimating Hemispheres

1. A hemisphere with radius 5 units fits snugly into a cylinder of the same radius and height.
1. Calculate the volume of the cylinder.
2. Estimate the volume of the hemisphere. Explain your reasoning.

SLIDESMANIA.COM

23.3 Estimating Hemispheres

• A cone fits snugly inside a hemisphere, and they share a radius of 5.
• What is the volume of the cone?
• Estimate the volume of the hemisphere. Explain your reasoning.

​

​

​

​

​

• Compare your estimate for the hemisphere with the cone inside to your estimate of the hemisphere inside the cylinder. How do they compare to the volumes of the cylinder and the cone?

SLIDESMANIA.COM

Lesson Summary

We know how to find the volume of (a cone and cylinder) to try and estimate the volume of a figure we do not know how to find the volume of (a sphere). In the next lesson, we will do something similar to learn how to find the volume of a sphere and see how close our reasoning today was to the actual calculation.

SLIDESMANIA.COM

A hemisphere-shaped security mirror fits exactly inside a rectangular prism box with a square base that has edge length 10 inches. What is a reasonable estimate for the volume of this mirror?

23.4 Cool Down: A Mirror Box

SLIDESMANIA.COM

Reflections

• Can you estimate the volume of a hemisphere by calculating the volume of shape I know is larger and the volume of a shape I know is smaller?

SLIDESMANIA.COM

Practice Problems

Must do: All problems

​

SLIDESMANIA.COM

Lesson Video

SLIDESMANIA.COM