Question

small cubes of edge 2cm are to be packed into a rectangular container measuring 6cm by 5m and 4m .How many cubes are required?

Answer 1

Answer:

$\bigstar{\bold{Number\:of\:cubes=15}}$

Step-by-step explanation:

$\Large{\underline{\sf{Given:}}}$

• Edge of small cube = 2 cm
• Dimensions of the rectangular container = 6 cm × 5 cm × 4 cm

$\Large{\underline{\sf{To\:Find:}}}$

• Number of cubes that are required

$\Large{\underline{\sf{Solution:}}}$

➵ Here we have to find how many cubes can be packed into the rectangular container.

➵ First we have to find the volume of the cube.

➵ Volume of a cube is given by,

    Volume of a cube = a³

    where a is a side of the cube

➵ Substitute the data,

    Volume of the cube = 2³

    Volume of the cube = 8 cm³

➵ Hence volume of each of the cube is 2 cm³.

➵ Now finding the volume of the rectangular container which is in the shape of a cuboid,

➵ Volume of a cuboid is given by,

    Volume of a cuboid = l × b × h

    where l is the length

    b is the breadth

    h is the height

➵ Substitute the data,

    Volume of rectangular container = 6 × 5 × 4

    Volume of rectangular container = 120 cm³

➵ Hence volume of the container is 120 cm³.

➵ Now finding the number of cubes that can be packed into it,

➵ Number of cubes = Volume of container/Volume of cube

➵ Substituting the data,

    Number of cubes = 120/8

    Number of cubes = 15

➵ Hence 15 cubes can be packed inside the rectangular container.

    $\boxed{\bold{Number\:of\:cubes=15}}$

Answer 2

Given:

• Edge of cube = 2 cm

• Length of rectanglular container = 6 cm
• Breadth of Rectanglular container = 5 cm
• Height of Rectanglular container = 4 cm

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To find:

• Number of cube required?

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Solution:

• Edge of cube = 2 cm

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We know that,

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$\star\;{\boxed{\sf{\purple{Volume_{\;(cube)} = (edge)^3}}}}$

Therefore,

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$\qquad\quad:\implies (2)^3$

$\qquad:\implies{\boxed{\sf{\pink{8\;cm^3}}}}\;\bigstar$

Now, We have to find, Volume of Rectanglular container (cuboidal) :]

$\star\;{\boxed{\sf{\purple{Volume_{\;(cuboid)} = l \times b \times h}}}}$

$\quad:\implies\sf 6 \times 5 \times 4$

$\qquad:\implies{\boxed{\sf{\pink{120\;cm^3}}}}\;\bigstar$

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$\underline{\bigstar\:\boldsymbol{According\:to\: the\:question\::}}$

• Small cubes are to be packed into a rectangular container.

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$:\implies\sf No.\;of\;cubes = \dfrac{Volume\;of\; container}{Volume\;of\;one\;cubes}$

$\qquad\:\:\:\::\implies\sf \cancel{\dfrac{120}{8}}$

$\qquad:\implies{\boxed{\sf{\pink{15\;cubes}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;15\;cubes\;are\; required\;to\;pack\;into\; container.}}}$