Real Life Problems involving Area

Transcription

1 Rel Life Prolems involving Are Prolems occur often in everydy life. Exmple :- A edroom wll is to e wllppered. (300 cm) The wll hs een mesured nd is 6 metres y etres, s shown. The rolls of wllpper to e used mesure 60 cm wide nd hve length of 11 metres when unrolled. The wllpper costs per roll. 60 cm 6 m (600 cm) Step 1 :- Step 2 :- Find how mny strips cn e cut from 1 roll. one roll = 11 m = 3 full strips (with it left over). Discuss why you might need extr pper? (Hint :- hve look t the pttern of the pper). Find how mny rolls you would need = 10 strips But 1 roll gives 3 strips! You would need 4 rolls to cover the wll. Step 3 :- Clculte the cost. 4 x = Discuss wht other costs re involved in wllppering wll. (Hint :- Wht keeps the pper on the wll? Wht tools/items do you need?) Exercise 1 1. Using the sme rolls of wllpper ove, find how mny strips, how mny strips per roll, how mny rolls re needed nd the cost of wllppering this wll. 2. Using the sme wllpper s question 1, find the cost of wllppering rectngulr wll :- 15 m 8 m long y 250 cm high 7 metres long y 2 etres high. Ntionl 4 Lifeskills - Geometry & Mesure pge 184 Chpter 23 - Prolem Solving

2 3. A rectngulr kitchen floor, 5 m y, is to e tiled using squre tiles of side 50 cm. 5 m How mny tiles will e needed to tile the floor? The tiles cost for ech pck of ten. How much will the tiles cost in totl? 50 cm 50 cm 4. This floor is to e tiled using squre tiles of side 30 cm. 2 (230 cm) These tiles cost per pck of eight tiles. How much will it cost to tile the floor? (Rememer - if you need prt of tile, count it s full tile). 3 6 m (360 cm) 5. A throom wll is to e tiled. The wll hs dimensions s shown. Ech tile used is 40 cm y 40 cm. The tiles re sold in oxes of twenty t 56 per ox. 270 cm window 120 cm 80 cm How much will it cost to uy the tiles for this wll? 40 cm 40 cm 400 cm 6. Tni hs to pint the outside wlls of her grden shed which is in the shpe of cuoid mesuring y 2 5 m y 2 m. 1 m 50 cm 2 m There is only one window (shown) which mesures 1 m y 50 cm. A one litre tin of pint covers 6 m m The pint costs 6 95 per tin. Wht will e the totl cost of the pint? 7. A plyground is in the shpe of lrge squre nd right ngled tringle s shown. The plyground is to hve its surfce covered in specil wether resistnt ruerised mteril. This mteril costs 108 per squre metre. How much will it cost to cover the plyground with the specil wether resistnt mteril? 6 m 1 Ntionl 4 Lifeskills - Geometry & Mesure pge 185 Chpter 23 - Prolem Solving

3 Extension questions :- You my find questions 8 to 10 difficult - ut try them. 8. Mr Simpson hs grge in the shpe of cuoid. He decided to convert his grge into ply room. He ricks over the grge door, plsters ll 4 wlls nd prepres to cover them with yellow wllpper. 240 cm Ech roll hs width 60 cm nd hs length of 10 metres. The wllpper costs 8 95 per roll. Find how mny strips of wllpper, nd hence how mny rolls he needs to wllpper the 4 wlls of the new room. Clculte the totl cost of the wllpper. 6 m Forget doors nd windows. 9. The Grnd Hotel hs rectngulr llroom 60 m y 40 m. The Bllroom is to e crpeted. Ech roll of crpet is wide nd when unrolled is 2 long. Wht is the minimum numer of rolls required to crpet the llroom? Crpets & Co give the following estimte :- Ech roll costs The jo will tke 15 hours to complete. The dditionl costs re s follows :- 6 crpet 24 per hour ech Mchinery hire 40 per hour. How much will it cost the Hotel to crpet the llroom? 40 m 60 m c Crpets-R-Us cn fit one-piece crpet 60 m y 40 m. This will cost 5% more thn Crpets & Co s totl estimte for the ctul cost of the crpet. They estimte it only will tke 12 hours, using 4 men t 25 per hour using the sme mchinery. How much re Crpets-R-Us quoting? d The Hotel use Crpet-R-Us to crpet their llroom. Why do you think they chose this compny? 10. Find the re of your clssroom floor. Investigte the cost to cover the floor with different types of flooring. Find the re of one of the wlls in your clssroom. Investigte the cost of tiling this re with different types of tiles. c Write report or cost proposl on your findings for nd. Ntionl 4 Lifeskills - Geometry & Mesure pge 186 Chpter 23 - Prolem Solving

4 Rel Life Prolems involving Volume Prolems, involving spce nd volume occur often in everydy life. Exmple :- A delivery vn hs storge spce which is in the shpe of cuoid, y y 3 5 m tll. How mny oxes 50 cm y 50 cm y 50 cm will fit into the vn? Step 1 :- Find how mny oxes will fit long one side of the vn. () 400 cm 50 cm = 8 oxes. Step 2 :- Find how mny will sit on the floor in totl. () 300 cm 50 cm = 6 there cn e 6 rows => 48 oxes. Step 3 :- Find how mny lyers stcked on top you cn hve. (3 5 m) 350 cm 50 cm = 7 stcks high Step 4 :- Find totl numer of oxes. 8 x 6 x 7 = 336. The vn cn hold 336 oxes. N.B. The vn is completely full - no spces. Exercise 2 All oxes nd continers re cuoidl unless otherwise stted. 1. A smller vn hs storge spce 2 m y 2 m y 1 m high. (Boxes cnnot e stored ove the 1 metre height). How mny oxes cn the vn hold if the oxes mesure :- 25 cm y 25 cm y 25 cm 50 cm y 25 cm y 20 cm? 2. A storge depot in Aerdeen hs to deliver three hundred oxes to its Dundee depot. The vn from question 1 is used. The oxes this time re 40 cm y 30 cm y 30 cm. (This time there is some empty spce on the vn). How mny trips will the vn hve to mke to deliver ll 300 oxes? Ntionl 4 Lifeskills - Geometry & Mesure pge 187 Chpter 23 - Prolem Solving

5 3. DVD cses 2 cm wide re stcked long shelf. How mny cses cn e stcked long shelf 2 metres long? Wht is the minimum length of shelf needed to stck 120 DVDs? 4. A vn hs storge cpcity of 450 cm y 300 cm y 200 cm. How mny Plsm TV oxes 150 cm y 100 cm y 20 cm cn e put into the vn? How mny toy oxes 40 cm y 40 cm y 40 cm cn e put into the vn? 5. Sirloin steks re pcked into oxes 20 cm y 20 cm y 10 cm. The oxes re to e put into seled freezer unit 100 cm y 80 cm y 60 cm. How mny oxes cn e pcked into ech freezer unit? 6. Wooden roof joists re stored in rn mesuring 30 m long y 9 m wide y high. Ech joist is 6 m long, 30 cm wide nd hs depth of 10 cm. Wht is the mximum numer of joists tht cn e stored in the rn? (Disregrd the roof spce). 7. The continer on the truck elow mesures 8 m y y wide. 8 m How mny oxes 40 cm y 40 cm y 40 cm cn e put onto this truck? How mny oxes 75 cm y 80 cm y 65 cm cn e put in this truck? Ntionl 4 Lifeskills - Geometry & Mesure pge 188 Chpter 23 - Prolem Solving

6 Extension questions :- You my find questions 8 to 11 difficult - ut try them. 8. A lrge crgo ship s hold crries 200 continers. Ech continer is 8 m y 5 m y. Ech continer is full of identicl crtes. Ech crte mesures 1 m y 50 cm y 50 cm. Ech crte is full of identicl oxes. Ech ox, 25 cm y 25 cm y 25 cm, contins Teddy Ber. 5 m 8 m How mny Teddy Bers re on the ship? 9. A lrge cn of Cole Col hs dimensions s shown. How mny cns (upright) cn e put into ox 48 cm y 40 cm y 120 cm tll? c Explin why this size of ox is etter thn ox mesuring 60 cm y 35 cm y 135 cm tll. The oxes in re trnsported y trucks which hve storge cpcity of 5 m y y 3 6 m tll. 12 cm 20 cm 120 cm 40 cm 48 cm How mny trips would the truck need to mke to trnsport one million cns? 10. A room mesures 6 metres y 6 metres. Tony is going to tile it with pink nd lue tiles. The lue tiles mesure 50 cm y 50 cm. The pink tiles mesure 25 cm y 25 cm. He strts to drw out on pper the pttern shown. Mke scle drwing on squred pper showing the lue nd pink tiles, following this pttern. How mny pink tiles does he need? Tony finds he hs to hlve some of the lue tiles, ut cn use oth hlves to fill in the gps. c How mny lue tiles is Tony going to need? Both tiles re sold in pcks of 6, the lue ones costing per pck nd the pink ones costing 5 95 per pck. d Clculte the totl cost for ll the tiles. Ntionl 4 Lifeskills - Geometry & Mesure pge 189 Chpter 23 - Prolem Solving