WISKUNDIGE GELETTERDHEID
GRAAD 10
NOG OEFENINGE
  
Buite-oppervlakte en volume van liggame.
  
MATHEMATICAL LITERACY
GRADE 10
MORE EXERCISES
  
Surface area and volume of regular bodies .
  
  
Vraag  / Question  1  
  
         Jy mag die volgende formules
         gebruik om onderstaande vrae
         te beantwoord :
         You may use the following formulae to
         answer to questions below :
  
  
         Gebruik die volgende afkortings :          Use the following abbreviations :
  
         Lengte / Length = l ;                             Breedte / Breadth / Width = b
 ;        Hoogte / Height = h                             basis / base = b ; 
          Middellyn / Diameter = d ;                   straal / radius / radius = r 
         sy / side  =  s ;                                    Vertikale hoogte / Vertical height = H ;
  
         Liggaam / Body                     Buite-oppervlakte ( BO ) /               Volume
                                                          Surface area ( SA )
  
         Reghoekige prisma /              BO / SA = 2(l + b)h + 2lb               V = lbh
         Rectanglular prism
  
         Kubus / Cube                               BO / SA = 6s2                          V = s3
  
         Driehoekige prisma /          BO / SA = (s1 + s2 + s3)l + bh           V = ½bhl
         Trianglular prism
  
                                                                                                                               4
         Sfeer/bal/ Sphere/ball              BO / SA = 4 π r2                          V = ── πr3
                                                                                                                               3
  
         Silinder / Cylinder                    BO / SA = 2πrh + 2πr2                  V = πr3h
                              
         Keël / Cone                            BO / SA = 4 π r2 + π rl                 V = ⅓ πr2H
  
         Piramiede / Pyramid                BO / SA = 2sh + s2                      V = ⅓ s3H
  
         Bereken die buite-oppervlakte en volume van elke liggaam :
         Calculate the surface area and volume of every body :
  
  
  

                             [ A 1. ]                          [ A 2. ]                              [ A 3. ]
  
  
  

                             [ A 4. ]                          [ A 5. ]                              [ A 6. ]
  
  
  

                                     [ A 7. ]                          [ A 8. ]                              [ A 9. ]
  
  
  

                             [ A 10. ]                          [ A 11. ]                              [ A 12. ]
  
  
  

                                   [ A 13. ]                                                  [ A 14. ]
  
  
  
   15.  Ses lood sfere met
          radius 1,5 cm word gesmelt en
          dan in 'n reghoekige vorm met
          lengte 7 cm en breedte 4 cm,
          gegooi. Bereken die hoogte van
          die lood in die vorm.
                                                     [ A 15. ]
  
   16.  'n Silindriese tenk, middellyn = 2 m
          en hoogte = 3 m, vang reënwater op.
          Na 'n bui is die tenk ¾ vol.
          Bereken die volume van die water
          in die tenk in m3 en in liter
          as 1 m3 = 1 000 ℓ
                                                     [ A 16. ]
  
   17.  'n Reghoekige metaalplaat, 98 dm
          lank en 13 dm breed, word gerol
          om 'n oop silinder te vorm.
  17.1   Bereken die radius van die silinder.
                                                     [ A 17.1 ]
  
   17.2  Die silinder word nou van 'n
            boom maar nie 'n deksel voorsien.
            Bereken die volume water, in ℓ,
            wat die silinder kan bevat.
                                                     [ A 17.2 ]
  
  
   18.  'n Piramiede het 'n vierkantige basis met
          oppervlakte 16 m2. Die vertikale hoogte
          is 3 m en die skuinshoogte is 3,6 m.
          Bereken die volume van die piramiede.
                                                     [ A 18. ]
  
  
   19.  Willem wil 'n kegelvormige wigwam bou.
          Die vloer het 'n middellyn van 4 m, die
          loodregte hoogte is 2,5 m en die skuinshoogte
          is 3,2 m. Bereken die lengte van die
          seilmateriaal wat Willem moet koop om
          die wigwam te bou. Die materiaal
          is 4 m wyd.
                                                     [ A 19. ]
  
  
   15.  Six lead spheres with a radius
          of 1,5 cm are melted and the
          molted lead is then cast into a
          rectangular form with length 7 cm
          and breadth 4 cm. Calculate the
          height of the lead in the form.
                                                          [ A 15. ]
  
   16.  A cylindrical tank, diameter = 2 m
          and height = 3 m, is used to collect
          rainwater from a roof. After one rainstorm
          the tank is ¾ full.
          Calculate the volume of the water in
          the tank in m3 and in litres if 1 m3 = 1 000 ℓ
                                                          [ A 16. ]
  
   17.  A rectangular metal sheet, 98 dm long
          and 13 dm wide, is rolled to form an
          open cylinder.
   17.1   Calculate the radius of this cylinder.
                                                          [ A 17.1 ]
  
   17.2   The cylinder is now fitted with a bottom
             but no lid. Calculate the volume of water,
             in ℓ, that this cylinder can contain.
                                                          [ A 17.2 ]
  
  
  
   18.  A pyramid has a square base with an area
          of 16 m2. The perpendicular height of the
          pyramid is 3 m and the slant height is 3,6 m.
          Calculate the volume of the pyramid.
                                                          [ A 18. ]
  
  
   19.  William wants to make a conical
          shaped wigwam. The floor has a
          diameter of 4 m, the vertical height
          is 2,5 m and the slant height is 3,2 m.
          Calculate the length of the canvas that
          William has to buy to make the wigwam.
          The width of the canvas is 4 m.
                                                          [ A 19. ]