Question

3. A cuboid is of dimensions (60*50*30)cm .How many small cubes with side 6 cm can be placed in the given cuboid?
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Answer 1

Answer:

Volume of the cuboid =L×B×H

volume of the cuboid =60×50×30

volume of the cuboid =90000 cm³

volume of the cube =a³

volume of the cube =6×6×6

volume of the cube =216 cm³

No of cubes that can be fitted =

volume of cube/volume of cuboid

90000/216= 416

Answer 2

$\large{\underline{\underline{\pmb{\sf{\; Understanding\; the\; question\;:}}}}}$

• Here, the concept of volume of a cuboid has been used. We're given with the dimensions of a cuboid and side of a small cube. The volume of the cuboid into which cubes is to be placed is obviously larger than the volume of the cube which is to be placed inside. So, in order to find how many cubes can be placed inside the cuboid. We firstly need to calculate the volume of cube and cuboid then dividing the volume of cuboid by the volume of cube. So, let's firstly examine the formulas for volume of cube and cuboid.

$\large{\underline{\underline{\pmb{\sf{\; Formula\; used\;:}}}}}$

» Here, we've to use the volume of cuboid and volume of cube. Volume of cuboid is the product of it's dimensions in essence, length, breadth and height. It is given by:

$\qquad\star~{\underline{\boxed{\pmb{\frak{Volume\; of\; cuboid=lbh}}}}}$

» Now, the volume of cube. Volume of cube is product of it's dimensions, as the cube has same dimensions so the formula is given by:

$\qquad\star~{\underline{\boxed{\pmb{\frak{Volume\; of\; cube={a}^{3}}}}}}$

$\begin{gathered}\rule{230px}{.2ex}\\\end{gathered}$

$\large{\underline{\underline{\pmb{\sf{\; Solution\;:}}}}}$

Given that, the dimensions of cuboid is 60 × 50 × 30 cm. The small cubes has sides of 6 cm.

To Attain, how many cubes can be placed in the cuboid.

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

⟩⟩ Let's firstly find the volume of cuboid. We know,

$:\implies\quad\sf{{Volume}_{(Cuboid)}=lbh}$

$\\:\implies\quad\sf{{Volume}_{(Cuboid)}=60\times 50\times 30}$

$\\:\implies\quad\underline{\pmb{\sf{{Volume}_{(Cuboid)}=90,000\; {cm}^{3}}}}$

⟩⟩ Now, let's calculate the volume of cube. We know:

$:\implies\quad\sf{{Volume}_{(Cube)}={(6)}^{3}}$

$\\:\implies\quad\underline{\pmb{\sf{{Volume}_{(Cube)}=216\; {cm}^{3}}}}$

↠ㅤNow, according to the question, we've been asked to calculate that how many small cubes with side 6 cm can be placed in the given cuboid. So,

$:\implies\quad\sf{{Total}_{(Cubes)}=\dfrac{{Volume}_{(Cuboid)}}{{Volume}_{(Cube)}}}$

$\\:\implies\quad\sf{{Total}_{(Cubes)}=\dfrac{90,000}{216}}$

$\\:\implies\quad\sf{{Total}_{(Cubes)}=416.6666}$

$\\:\implies\quad\underline{\boxed{\pmb{\frak{{Total}_{(Cubes)}\approx 416\; cubes}}}}$

❝Therefore, 416 cubes can be placed in the cuboid.❞