Popcorn Prisms

Surface Area Surface Area & Volume& Volume

To do the next two lessons, you need to know...

•That a prism is a 3-dimensional shape with 2 identical parallel bases.

•The formulas for SA (surface area) and for V (volume) of a rectangular prism and a cylinder.

Let’s start in the beginning…

Before you can do surface area or volume, you have to know the following formulas.

Rectangle A = lw

Circle A = πr²

C = πd

Let’s start with a rectangular prism.

Surface area can be done using the formula

SA = 2 lw + 2 lw + 2 lw OR

Either method will give you the same answer.

you can find the area for each surface and add them up.

Volume of a rectangular prism is V = lwh

Example:

7 cm

4 cm

8 cm Surface Area

Front/back 2(8)(4) = 64 cm²

Left/right 2(4)(7) = 56 cm²

Top/bottom 2(8)(7) = 112 cm²

Add them up!

SA = 232 cm²

Volume

V = lwh

V = 8(4)(7)

V = 224 cm³

CIRCLESYou must know the difference between RADIUS and DIAMETER.

r

d

Center of the circle

SURFACE AREA of a CYLINDER.

You can see that the surface is made up of two circles and a rectangle.

The length of the rectangle is the same as the circumference of the circle!

Imagine that you can open up a cylinder like so

EXAMPLE: Round to the nearest TENTH.

Top or bottom circle

A = πr²

A = π(3.1)²

A = π(9.61)

A = 30.2 cm²

Rectangle

C = length

C = π d

C = π(6.2)

C = 19.5 cm

Now the area

A = lw

A = 19.5(12)

A = 234 cm²

Now add:

30.2 + 30.2 + 234 =

SA = 294.4 in²

There is also a formula to find surface area of a cylinder.

Some people find this way easier:

SA = 2πrh + 2πr²

SA = 2π(3.1)(12) + 2π(3.1)²

SA = 2π (37.2) + 2π(9.61)

SA = π(74.4) + π(19.2)

SA = 233.7 + 60.4

SA = 294.1 in²

The answers are REALLY close, but not exactly the same. That’s because we rounded in the problem.

Find the radius and height of the cylinder.

The formula tells you what to do!!!!

Remember the order of operations. You multiply before you add.

2πrh + 2πr² means multiply 2(π)(r)(h) + 2(π)(r)(r)

V = (πr²)(h)

V = (π)(3.1²)(12)

V = (π)(3.1)(3.1)(12)

V = 396.3 in³

Volume of a Cylinder

We used this drawing for our surface area example. Now we will find the volume.

optional step!

ARE YOU READY?Let’s see what you can do with

POPCORN PRISMS!

YUM!!