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?

Video Solution
Cubes And Cube Roots
Ex 7.1 | Question 4

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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