Geometry Formulas: Surface Area & Volume

A formula is just a set of instructions A formula is just a set of instructions. It tells you exactly what to do! All you have to do is look at the picture and identify the parts. Substitute numbers for the variables and do the math. That’s it! 

Either method will gve you the same answer. Let’s start with a rectangular prism. Surface area can be done using the formula SA = 2 lw + 2 wl + 2 lw OR Either method will gve 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 Front/back 2(8)(4) = 64 Left/right 2(4)(7) = 56 Top/bottom 2(8)(7) = 112 Add them up! SA = 232 cm² V = lwh V = 8(4)(7) V = 224 cm³

SURFACE AREA of a CYLINDER. Imagine that you can open up a cylinder like so: 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!

EXAMPLE: Round to the nearest TENTH. Top or bottom circle A = πr² A = π(3.1)² A = π(9.61) A = 30.2 Rectangle C = length C = π d C = π(6.2) C = 19.5 Now the area A = lw A = 19.5(12) A = 234 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.

The formula tells you what to do!!!! Find the radius and height of the cylinder. Then “Plug and Chug”… Just plug in the numbers then do the math. Remember the order of operations and you’re ready to go. The formula tells you what to do!!!! 2πrh + 2πr² means multiply 2(π)(r)(h) + 2(π)(r)(r)

Cylinder V = (πr²)(H) Volume of Prisms or Cylinders You already know how to find the volume of a rectangular prism: V = lwh The new formulas you need are: H = the height of the cylinder Cylinder V = (πr²)(H)

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. V = (πr²)(H) V = (π)(3.1²)(12) V = (π)(3.1)(3.1)(12) V = 396.3 in³ optional step!

V = (πr²)(H) V = (π)(4²)(10) V = (π)(16)(10) V = 502.7 m³ Try one: d = 8 m V = (πr²)(H) V = (π)(4²)(10) V = (π)(16)(10) V = 502.7 m³ Since d = 8, then r = 4 r² = 4² = 4(4) = 16

Here are the formulas you will need to know: A = lw SA = 2πrh + 2πr² A = ½ bh V = (½ bh)(H) A = π r² V = (πr²)(H) C = πd and how to find the surface area of a prism by adding up the areas of all the surfaces