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The figure M shows a cylindrical bucket of diameter 28cm and height 100cm while figure N shows a jug which can hold 2.2 litres of water when completely full. (a) Calculate the amount of water in litres the bucket M can hold. (Use pi = 22/7) (b) How many jugs N can be enough to fill the bucket M?

Mathematics

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Haya Exodus, twende kazi.

28. a) Kokotoa kiasi cha maji katika lita ambacho ndoo M inaweza kushika.

  1. Tafuta radius ya ndoo M.

    Kipenyo (DD) = 28 cm
    Radius (rr) = D2=28 cm2=14 cm\frac{D}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm}

  2. Kokotoa ujazo wa ndoo M katika sentimita za ujazo (cm3cm^3).

    Urefu (hh) = 100 cm
    Tumia π=227\pi = \frac{22}{7}
    Fomula ya ujazo wa silinda ni V=πr2hV = \pi r^2 h.

    V=227×(14 cm)2×100 cmV = \frac{22}{7} \times (14 \text{ cm})^2 \times 100 \text{ cm} V=227×196 cm2×100 cmV = \frac{22}{7} \times 196 \text{ cm}^2 \times 100 \text{ cm} V=22×28×100 cm3V = 22 \times 28 \times 100 \text{ cm}^3 V=61600 cm3V = 61600 \text{ cm}^3
  3. Badilisha ujazo kutoka sentimita za ujazo kwenda lita.

    Tunajua kuwa 1 lita = 1000 cm3^3.

    Vlita=61600 cm31000 cm3/litaV_{\text{lita}} = \frac{61600 \text{ cm}^3}{1000 \text{ cm}^3/\text{lita}} Vlita=61.6 litaV_{\text{lita}} = 61.6 \text{ lita}

    Ndoo M inaweza kushika lita 61.6 za maji.

    61.6 lita\boxed{61.6 \text{ lita}}

    28. b) Jagi ngapi N zinaweza kutosha kujaza ndoo M?

  4. Tumia ujazo wa ndoo M na ujazo wa jagi N.

    Ujazo wa ndoo M = 61.6 lita (kutoka sehemu a)
    Ujazo wa jagi N = 2.2 lita (kutoka maelezo ya swali)

  5. Kokotoa idadi ya jagi zinazohitajika.

    Idadi ya jagi = Ujazo wa ndoo MUjazo wa jagi N\frac{\text{Ujazo wa ndoo M}}{\text{Ujazo wa jagi N}}

    Idadi ya jagi=61.6 lita2.2 lita\text{Idadi ya jagi} = \frac{61.6 \text{ lita}}{2.2 \text{ lita}} Idadi ya jagi=61622\text{Idadi ya jagi} = \frac{616}{22} Idadi ya jagi=28\text{Idadi ya jagi} = 28

    Jagi 28 N zinaweza kutosha kujaza ndoo M.

    28 jagi\boxed{28 \text{ jagi}}
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