2A 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!
3Rectangle A = b(h) Triangle A = b(h) 2 Circle A = π r² radius Let’s start in the beginning…Before you can do surface area or volume, you have to know the following formulas.Rectangle A = b(h)Triangle A = b(h)2Circle A = π r² radiusC = πd diameter
4VOLUME FORMULAS Rectangular Prism v=l x w x h (lwh) Cube v= s ^3 Cylinder v= x r^2 x hPI =3.14
5TRIANGLESYou can tell the base and height of a triangle by finding the right angle:
6CIRCLESYou must know the difference between RADIUS and DIAMETER.rd
7Either method will gve you the same answer. Let’s start with a rectangular prism.Surface area can be done using the formulaSA = 2 lw + 2 wl + 2 lw OREither 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
9To find the surface area of a triangular prism you need to be able to imagine that you can take the prism apart like so:Notice there are TWO congruent triangles and THREE rectangles. The rectangles may or may not all be the same.Find each area, then add.
103. The back rectangle is different Find the AREA of each SURFACE1. Top or bottom triangle:A = ½ bhA = ½ (6)(6)A = 182. The two dark sides are the same.A = lwA = 6(9)A = 54Example:8mm9mm6 mm mm3. The back rectangle is differentA = lwA = 8(9)A = 72ADD THEM ALL UP!SA = 216 mm²
11SURFACE 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!
12EXAMPLE: Round to the nearest TENTH. Top or bottom circleA = πr²A = π(3.1)²A = π(9.61)A = 30.2RectangleC = lengthC = π dC = π(6.2)C = 19.5Now the areaA = lwA = 19.5(12)A = 234Now add:=SA = in²
13There is also a formula to find surface area of a cylinder. Some people find this way easier:SA = 2πrh + 2πr²SA = 2π(3.1)(12) + 2π(3.1)²SA = 2π (37.2) + 2π(9.61)SA = π(74.4) + π(19.2)SA =SA = in²The answers are REALLY close, but not exactly the same. That’s because we rounded in the problem.
14The 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)
15Cylinder V = (πr²)(H) Volume of Prisms or Cylinders You already know how to find the volume of a rectangular prism: V = lwhThe new formulas you need are:Triangular Prism V = (½ bh)(H)h = the height of the triangle andH = the height of the cylinderCylinder V = (πr²)(H)
16V = 162 mm³ V = (½ bh)(H) V = ½(6)(6)(9) Volume of a Triangular Prism We used this drawing for our surface area example. Now we will find the volume.V = (½ bh)(H)V = ½(6)(6)(9)V = 162 mm³This is a right triangle, so the sides are also the base and height.Height of the prism
17V = 864 cm³ V = (½ bh)(H) V = (½)(12)(8)(18) Try one: Can you see the triangular bases?V = (½ bh)(H)V = (½)(12)(8)(18)V = 864 cm³Notice the prism is on its side. 18 cm is the HEIGHT of the prism. Picture if you turned it upward and you can see why it’s called “height”.
18V = (πr²)(H) V = (π)(3.1²)(12) V = (π)(3.1)(3.1)(12) V = 396.3 in³ Volume of a CylinderWe 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 = in³optional step!
19V = (πr²)(H) V = (π)(4²)(10) V = (π)(16)(10) V = 502.7 m³ Try one: d = 8 mV = (πr²)(H)V = (π)(4²)(10)V = (π)(16)(10)V = m³Since d = 8,then r = 4r² = 4² = 4(4) = 16
20Here are the formulas you will need to know: A = lw SA = 2πrh + 2πr²A = ½ bh V = (½ bh)(H)A = π r² V = (πr²)(H)C = πdand how to find the surface area of a prism by adding up the areas of all the surfaces