Pencil box measuring 20cm × 12cm × 8cm are packed in a wooden box measuring 144cm × 20cm × 10cm . How many pencil boxes are packed in a wood

Question

Pencil box measuring 20cm × 12cm × 8cm are packed in a wooden box measuring 144cm × 20cm × 10cm . How many pencil boxes are packed in a wooden box​

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Natalia 4 weeks 2021-08-14T08:39:23+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-08-14T08:41:02+00:00

    Answer:

    \huge\underline\bold {Answer:}

    Volume of wooden box = l × b × h

    = 144 × 20 × 10 = 28800 centimetre cube.

    Volume of pencil box = l × b × h

    = 20 × 12 × 8

    = 1920 centimetre cube.

    Therefore, number of pencil boxes packed in the wooden box = Volume of wooden box ÷ Volume of pencil box

    = 28800 ÷ 1920

    = 15

    Therefore, 15 pencil boxes are packed in the wooden box.

    0
    2021-08-14T08:41:19+00:00
    • 15 pencil boxes are packed in a wooden box.

    Given :–

    • Measure of pencil box = 20cm × 12cm × 8cm.
    • Measure of wooden box = 144cm × 20cm × 10cm.

    To Find :–

    • Number of pencil boxes are packed in a wooden box.

    Solution :–

    Pencil and wooden box is a cuboid.

    So we know that,

    Volume of cuboid,

     \longmapsto \sf \green{length \times breadth \times height}

    First, we need to find the volume of pencil and wooden box.

    For pencil box,

    • Length = 20cm.
    • Breadth = 12cm.
    • Height = 8cm.

    So,

     \mapsto 20cm\times 12cm \times 8cm

     \mapsto20cm \times 96 {cm}^{2}

     \mapsto1920 {cm}^{3}

    Now, we need to find the volume of wooden box.

    We have,

    • Length = 144cm.
    • Breadth = 20cm.
    • Height = 10cm.

    So,

     \mapsto144cm \times 20cm \times 10cm

     \mapsto144cm \times 200 {cm}^{2}

     \mapsto28800 {cm}^{3}

    Now, we have to find the number of pencil boxes are packed in a wooden box.

    So,

    Number of pencil boxes,

     \longmapsto \sf \green{\dfrac{Volume \: of \: wooden \: box}{Volume \: of \: pencil \: box}}

    We have,

    • Volume of wooden box =  \sf 28800 {cm}^{3}
    • Volume of pencil box =  \sf 1920 {cm}^{3}

      \mapsto\dfrac{2880 \cancel{0} \cancel{{cm}^{3} }}{ 192\cancel{0 } \cancel{{cm}^{3}} }

      \mapsto \cancel\dfrac{ 2880}{192}

     \mapsto \cancel \dfrac{1440}{96}

     \mapsto\cancel\dfrac{720}{ 48}

     \mapsto\cancel\dfrac{360}{24}

     \mapsto \cancel\dfrac{180}{12}

       \mapsto \cancel\dfrac{ 90}{6}

     \mapsto \cancel\dfrac{ {45}}{ {3} }

     \mapsto\dfrac{15}{1}

      \mapsto 15

    Hence,

    The 15 pencil boxes are packed in a wooden box.

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