Join the Geometrics Stage Crew
in solving geometry challenges
based in your home:
rock the area of your bedroom walls
Cover the surface area of your bed
maximize the volume of your closet space
wArm-uP: select from the terms below and correctly fill in the blanks.
Cone surFACe AreA Cylinder Volume AreA
1. Measuring the space inside a two-dimensional shape determines: ______________
2. Measuring all the surfaces of a three-dimensional shape determines: ______________
3. Measuring the space inside a three-dimensional shape determines: ______________
4. What object has two bases and has a volume measured by height, radius, and pi?______________
5. What object can have the same height and radius as a cylinder but is 1/3 the volume? ______________
what is an Actuary? An actuary is an expert in statistics who
works with businesses, governments, and organizations to help
them plan for the future. Actuarial science is the discipline that
applies math and statistical methods to assess risk.
Take-Home Activity 1 Name: ____________________________________________________ Date: ____________
Use what you’ve learned about perimeter
and area to take some measurements in your
home. Assume you’re going to hang a few b
Geometrics posters in your room. You’ll need a
ruler and a calculator.
1 Pick a wall and calculate its perimeter and area.
2 The Geometrics Stage Crew gives you 10 rectangular posters that measure 8 1/2 inches by 11 inches, plus 5 circular posters
with a 1-foot radius, and one triangular poster with a base of 3 feet and a height of 3 feet. What is the total area of these
posters, and can you estimate how many will fit on your wall at home? note: The conversion box below of feet to inches
will help when calculating measurements for this activity and for Activities 2 and 3.
Area of rectangular posters: FeeT To ConVerTinG FeeT To inCHes
+ Area of circular posters: 1 foot = 12 inches
+ Area of triangular poster: 1 square foot = 144 square inches
= Total area of posters: 1 cubic foot = 1,728 cubic inches
Area of your bedroom wall: FeATured FormulAs
Area of 2d shapes:
- Total area of all posters:
Rectangle: A = l • w
Triangle: A = 1/2 • (b • h)
= Total remaining area on your wall: Circle: A = p • r2
The Geometrics stage Crew wants to make some circular welcome mats that promote
now Try THis: the band. They have to be the size of a doorway. Measure the width of the entranceway to
your bedroom. Using that measurement as the diameter, what would be the circumference and area of these rugs?
Take-Home Activity 2 Name: ____________________________________________________ Date: ____________
You can use the same skills at home that
the Geometrics Stage Crew uses to do their job.
Figuring out surface area can help you do things
like paint objects or calculate how much fabric is
needed to cover a bed. Solve the hypothetical
exercises below to see how surface h
area formulas might be used at home. h
1 You have a CD rack at home, which is a rectangular prism
that measures 3 feet long by 3 feet high with a width of
1 foot. How many square feet would you be painting to
surface Area of 3d shapes:
cover the two sides, the top, and the back?
Rectangular Prism: SA = 2 • (l • w + l • h + w • h)
Cone: SA = (p • r2) + (p • r • slant)
2 The Geometrics Stage Crew is selling cover sheets for beds that have the band’s logo on them. A full-size mattress
measures 54 inches wide by 75 inches long by 6 inches high. If the sheet were to cover all but the bottom of the
mattress, what is the minimum total surface area? State your answer in square feet.
At Geometrics shows, some fans wear cone-shaped hats because of the band’s
now Try THis: fondness for shapes. you decide to join in and paint a birthday hat you have at home.
You have a 1-ounce jar of gold paint, which will cover about 33 square inches. You have a hat with the measurements of
d = 4 inches and slant = 7 inches. Do you have enough paint to cover the hat? To figure this out you need to use the
formula for the surface area of a cone: SA = (p • r2) + (p • r • slant). Hint: You don’t need the (p • r2) part of the formula
because that’s the open circle part that will fit on your head.
Take-Home Activity 3 Name: _____________________________________________________ Date: ______________
The Perfect Fit
Just like the Geometrics Stage Crew used
volume measurement to fit props in a van,
you can apply volume measurement in and
around your home. For example, volume can
help you make sure you have enough room
for all your stuff. Try the exercises below to
see how it works.
Volume of 3d shapes:
Rectangular Prism: V = l • w • h
Cylinder: V = p • r2 • h
1 You have a CD collection and want a CD tower that will hold all of your
CDs. If the average CD measures about 6 inches long by 5 inches high by
1/4 (.25) inches wide, and you have 80 CDs, what should the minimum
volume of your CD rack be? You may want to use the conversion chart on
Activity 1 to calculate the cubic feet and cubic inches. Note: You’ll need
a calculator to figure out your answer.
2 To experiment more with cubic measurement, find out the volume of your bedroom and closet.
3 Volume is also great for measuring liquid. You may be able to figure out how much water a pool holds by getting
its length, width, and depth. The general rule is 1 cubic foot = 7.48 gallons. Assume your neighbors have a big,
perfectly round pool with a diameter of 30 feet and a depth of 5 feet. How much water would that pool hold?
You have a can of juice and want to find out how tall it is by using its radius and its volume.
now Try THis: Assume you pour the juice into a measuring glass and find that the can holds 12.1 ounces
of juice. If .55 ounces = 1 cubic inch, then 12.1 ounces = 22 cubic inches. Your can has a volume of 22 cubic inches and
a diameter of 2 inches. Using the cylinder formula on this page, calculate the height of the can rounded to the nearest
inch. Note: You’ll need a calculator to figure out your answer.