Enlargement 2. Scale and Enlargement

Transcription

1 Scle nd Enlrgement Enlrgement 2 Here is picture of Andy. He is 7 5 cm tll in the picture. In rel life, Andy is ctully twenty times the size he ppers to e in the picture. We sy tht this picture hs scle of 1 cm to 20 cm, which tells us tht the rel life Andy is twenty times the size of the one which we see here in the picture. (i.e. 20 x 7 5 = 150 cm) Exercise 1 1. Here re some scles. Wht numer would you hve to multiply ny mesurement y to rrive t the rel life size? 1 cm to 8 cm 1 m to 100 m c 1 m to 6 m d 1 cm to 1 metre e 1 : 9 ( one to nine ) f 1 : More scles. You would hve to divide ny rel length y the scle numer to reduce the rel life sitution into model or photogrph sitution. Wht would you divide y here to reduce the rel life to the model sitution : 1 cm to 10 cm 1 m to 50 m c 1 : 5 d 1 : 30 e 1 m to 10 km f 1 mm to 2 cm. creful 3. Use ruler to mesure these lines nd use the given scles to find the rel life distnce the lines represent : Scle 1 cm to 10 cm (length x 10) Scle 1 cm to 100 cm c Scle 1 : 10 d Scle 1 : 100 e f Scle 1 cm to 1 m Scle 1 cm to 1 km. Ntionl 4 Book N4-1 this is pge 225 Chpter 21 - Enlrgement 2

2 4. This model cr ws mde to scle of 1 cm to 50 cm.... cm Mesure the length of the cr in the drwing ove. Use the scle (1 cm = 50 cm) to find the length of the rel cr. 5. The model us is mde to the scle of 1 cm to 80 cm. Mesure the height of the us. Clculte the height of the rel us.... cm 6. The flgpole hs scle of 1 cm to 120 cm. Mesure the height of the flgpole. Clculte its rel height.... cm Ntionl 4 Book N4-1 this is pge 226 Chpter 21 - Enlrgement 2

3 7. The side of ech smll squre represents 50 cm in this scle drwing of greenhouse. POTS BEDDING PLANTS WORK BENCH X Y TOMATOES 50 cm 50 cm LETTUCE Clculte the rel length of : (i) the row of pots. (ii) the row of tomtoes. (iii) the trys of lettuce. (iv) the trys of edding plnts. The grdener wlks in stright line from his work ench (X) to the tomtoes (Y). How fr did he relly wlk? Clculting Lengths using Scles nd Scle Fctors Exmple : Solution :- A model vn is 8 centimetres long. The scle of the model is 1 : 50. (This mens tht the scle fctor for the question is 50). Clculte the rel length of the vn. Rel length of vn = 50 x model length = 50 x 8 cm = 400 cm (or 4 metres) Exercise 2 1. Clculte the rel lengths of these models, given their model lengths nd their scle fctors : A model us, length 10 cm. (Scle fctor 50). A model ship, length 20 cm. (Scle fctor 100). c A model stem engine, length 5 cm. (Scle fctor 200). d A model eroplne, length 12 cm. (Scle fctor 250). Ntionl 4 Book N4-1 this is pge 227 Chpter 21 - Enlrgement 2

4 2. A photogrph shows tht Chrlie is 15 cm tll. The scle of the drwing is 1 : 10. Wht is Chrlie s rel height? 3. Mry s foot is TWICE the length of her y sister s. Her sister s foot is 8 8 centimetres long. Write down the scle fctor here. Wht size re Mry s feet? 4. Hrold hs drwn up pln of his rectngulr grden. The drwing is 15 centimetres long nd 10 centimetres wide. The scle of his grden on the mp is given s 1 : 50. Write down the scle fctor. (i) Clculte the length of the ctul grden. (ii) Clculte the width of the ctul grden. Clculting Model Lengths knowing Scle Fctor Exmple : A vn is 400 cm long. A model of this vn is mde 50 times smller thn the ctul vn. Find the length of the model. (This time, though the scle is still 1 : 50, the scle fctor is 1 50 ). > This will reduce the length of the rel vn!!! Solution :- Length of model = x rel length = x 400 cm (= ) = 8 cm Ntionl 4 Book N4-1 this is pge 228 Chpter 21 - Enlrgement 2

5 5. Clculte the heights of these models, given their rel heights nd scle fctors : A vn 150 cm high. (Scle fctor 1 50 ) A lorry 300 cm high. (Scle fctor 1 50 ) c A icycle 120 cm high. (Scle fctor 1 2 ) d A trin 4 metres high. (Scle fctor ) e Mr Smith s house 5 metres high. (Scle fctor 1 20 ). 6. Sir Frncis hs model of his ycht on top of his dining room tle. The scle of the model is 1 : 20. If the length of his rel ycht is 15 metres, wht is the length of his model? 7. The girffe in this picture is 1 rel life size. 50 If the ctul girffe is 4 metres tll, wht will the height of the girffe in the picture e? 8. The scle of n ordinnce survey mp is 1 : Wht would the length of pth e on mp, if the rel length of the pth is 100 metres? 9. The two pictures shown elow re rectngulr. 12 cm reduced? cm 4 cm 32 cm The smller one is similr to the lrger, ut nturlly it hs een reduced in size. Look t the length of the longer side in ech rectngle nd stte y how much the lrger rectngle hs een reduced. ( 1 4, 1 2, 1...?) 5 Use this informtion to find the height of the smller rectngle mrked? cm. (Do not mesure it) Ntionl 4 Book N4-1 this is pge 229 Chpter 21 - Enlrgement 2

6 10. These crpets re similr, ut the second one is n enlrgement of the first one. 2 m? m 3 m 7 5 m Write down the scle fctor from the smller crpet to the lrger one. (It is not whole numer). Use this informtion to find the redth of the lrger crpet (mrked?). 11. These plying crds re similr. Write down the scle fctor from the smller crd to the lrger one. 6 cm x cm Use this informtion to find the length of the side of the crd mrked x cm. 4 cm 6 cm 12. Mother flmingo hs dughter who is n exct replic of herself, ut of course is smller. 90 cm 30 cm Mum Dughter If mother s height is 90 cm nd dughter s height is 30 cm, write down the scle fctor from mother to dughter. Mum s ek is 15 cm long. How long will the dughter s ek e? Ntionl 4 Book N4-1 this is pge 230 Chpter 21 - Enlrgement 2