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Alinda packed shoe polish tins (K) into the big box (L) shown below. Use them to answer the questions that follow. (a) If there were 3 layers packed in the box, find the value of i. (b) Calculate the total number of tins K that were parked in box L.

Mathematics

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2 parts
a

60 cm60 \text{ cm}

b

96 makopo96 \text{ makopo}

Step-by-step solution

6 steps

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Part 24

Alinda alipakia makopo ya rangi ya viatu (K) kwenye sanduku kubwa (L) kama inavyoonyeshwa hapa chini.

Part a

60 cm60 \text{ cm}

Ikiwa kulikuwa na tabaka 3 zilizopakiwa kwenye sanduku, tafuta thamani ya i.

  1. Tambua urefu wa kopo moja (K).

    Kutoka kwenye mchoro, urefu wa kopo K ni 20 cm.

  2. Kokotoa urefu wa sanduku (i) kwa tabaka 3.

    Ikiwa kuna tabaka 3 za makopo yaliyopangwa wima, urefu wa sanduku (i) utakuwa jumla ya urefu wa makopo hayo.

    i=Idadi ya tabaka×Urefu wa kopo mojai = \text{Idadi ya tabaka} \times \text{Urefu wa kopo moja} i=3×20 cmi = 3 \times 20 \text{ cm} i=60 cmi = 60 \text{ cm}

    Jibu la Swali la 24 (a):
    Thamani ya i ni: 60 cm\boxed{60 \text{ cm}}

Part b

96 makopo96 \text{ makopo}

Kokotoa jumla ya idadi ya makopo K yaliyopakiwa kwenye sanduku L.

  1. Tambua vipimo vya kopo K na sanduku L.

    Kopo K: Kipenyo = 10 cm, Urefu = 20 cm
    Sanduku L: Urefu = 80 cm, Upana = 40 cm, Urefu = 60 cm (kutoka sehemu a)

  2. Kokotoa idadi ya makopo yanayoweza kutoshea kwenye urefu na upana wa sanduku.

    Idadi ya makopo kwenye urefu wa sanduku = Urefu wa sandukuKipenyo cha kopo=80 cm10 cm=8\frac{\text{Urefu wa sanduku}}{\text{Kipenyo cha kopo}} = \frac{80 \text{ cm}}{10 \text{ cm}} = 8 makopo
    Idadi ya makopo kwenye upana wa sanduku = Upana wa sandukuKipenyo cha kopo=40 cm10 cm=4\frac{\text{Upana wa sanduku}}{\text{Kipenyo cha kopo}} = \frac{40 \text{ cm}}{10 \text{ cm}} = 4 makopo

  3. Kokotoa idadi ya makopo kwenye tabaka moja.

    Idadi ya makopo kwenye tabaka moja = (Idadi ya makopo kwenye urefu) ×\times (Idadi ya makopo kwenye upana)

    Makopo kwenye tabaka moja=8×4=32 makopo\text{Makopo kwenye tabaka moja} = 8 \times 4 = 32 \text{ makopo}
  4. Kokotoa jumla ya idadi ya makopo yaliyopakiwa.

    Kutoka sehemu (a), tunajua kuna tabaka 3.
    Jumla ya makopo = (Idadi ya makopo kwenye tabaka moja) ×\times (Idadi ya tabaka)

    Jumla ya makopo=32×3\text{Jumla ya makopo} = 32 \times 3 Jumla ya makopo=96 makopo\text{Jumla ya makopo} = 96 \text{ makopo}

    Jibu la Swali la 24 (b):
    Jumla ya idadi ya makopo K yaliyopakiwa kwenye sanduku L ni: 96 makopo\boxed{96 \text{ makopo}}

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