Maths Area and Volume

Maths Area and Volume

1. Perimeter

   • Key: dashed line=circle, solid line=perimeter of sector, dotted line=arc
   • Perimeter is adding up everything
     • To find the perimeter of the sector you need to add the two lengths with arc length
   • Arc length = theta/360 x 2pie x r
     • theta is the o with the squiggle
     • Other equations theta/360 x pieD
     • For examples go to handout

2. Area of a sector

   • theta/360 X pie X r squared
   • When you already have the area and you're looking for something else then first X360 to make a straight line and then use algebra skills

3. Volume

   • cuboid = lwh
   • cylinder = pie X r squared X h
   • prism = area of cross section X length
   • Pyramid = 1/3 X base area X height
     • May need Pythagoras to help
   • Cone = 1/3 X pie X r squared X height
   • Sphere = 4/3pie X r cubed
     • hemisphere/half sphere = 2/3pie X r cubed

4. Suraface area

   • For the surface area you need to add up the areas up of the shape e.g the bases and the rounded/curved area etc
   • Cylinder = curved surface area + top + bottom
     • Curved SA = 2pie X r X h
     • top and bottom = (pie X r squared) X2
   • Pyramid = base SA + triangle SA
     • Base SA = b X h
     • Triangle SA = 1/2 X b X h
     • If the base is uneven e.g 9 by 6 rather than 9 by 9 then you need to a front triangle and a side triangle
   • Cone = curved SA + base
     • Curved SA = pie X r X l
       • l = length of side
     • base = pie X r squared
   • Sphere = 4pie X r squared
     • hemisphere
       • without base = 2pie X r squared
       • with base = 3pie X r squared

5. compound shapes

   • Surface area
     • split the solid into the different shapes e.g base, curved cylinder, curved cone etc and then add the areas together to get the total surface area of the solid
       • don't add things you can't see e.g the base of the cone because you can't see it
   • Volume
     • split the solid into different shapes and work out their volume and then for the total volume you add up all the other volumes

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