Ex.7.1 Q4 Cubes and Cube Roots - NCERT Maths Class 8

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Question

Parikshit makes a cuboid of plasticine of sides \(5 \,\rm{cm},\) \(2 \,\rm{cm,}\) \(5\, \rm{cm.}\) How many such cuboids will he need to form a cube?

Text Solution

What is known?

Dimensions of cuboid \(5\;{\rm{cm}}\, \times\,2\;{\rm{cm}}\,\times \,5\;\rm{cm}.\)

What is unknown?

To find out the number of cuboids to form a cube.

Reasoning:

Number of cuboids required

\[\begin{align}=\frac{{{\text{Volume of cube}}}}{{{\text{Volume of cuboid}}}}\end{align}\]

Steps:

Volume of cuboid

\(\begin{align}&={\rm{length}}\! \times\! {\rm{breadth}} \\&\times {\rm{height}}\\
&= 5 \times 2 \times 5\\&= {5^2} \times {2^1}{\rm{c}}{{\rm{m}}^3}\end{align}\)

To make the volume of cuboid as a cube number we need to multiply it by \(5 \times 2 \times 2\)

\(\begin{align}&\text {Newly formed cube}\\&= {5^2} \times {2^1} \times 5\; \times 2 \times 2\\&= {5^3} \times {2^3}{\rm{c}}{{\rm{m}}^3}\end{align}\)

\(\begin{align}&\text {Number of cuboids required} \\&=\frac{5^{3} \times 2^{3}}{5^{2} \times 2}\\&=\frac{5 \times \not5 \times \not5 \times \not2 \times 2 \times 2}{\not 5 \times \not 5 \times \not2}\end{align}\)

\(\therefore \;\) Number of cuboids required to make a cube \(=\) \(\begin{align}5\times 2\times 2=20\end{align}\)

\(20\) cuboids required.

  
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