Question

Rahul makes a cuboid of plasticine of sides 3cm×3cm×5cm. how many such cuboid will he need to form a cube. plese explain me ​

Answer 1

Given

$\sf Let \ the \ length \ of \ the \ cuboid \ be \ 3 \ cm.$

$\sf Let \ the \ breadth \ of \ the \ cuboid \ be \ 3 \ cm.$

$\sf Let \ the \ length \ of \ the \ height \ be \ 5 \ cm.$

$\implies \bold{ \sf Volume \ of \ the \ cuboid } = l \times \ b \times h$

$= 3 \times 3 \times 5$

$= \underline{\underline{\sf 45 \ cm^{3} }}$

$\sf A \ cube \ has \ equal \ sides$

$\sf Each \ side \ of \ the \ cube = LCM \ of \ 3, \ 3 \ and \ 5$

$\mplies \sf Each \ side \ of \ the \ cube = 15 \ cm$

$\sf Volume \ of \ a \ cube = 15 \times 15 \times 15$

$\implies \underline{\underline{\sf 3375 \ cm^{3} }}$

$\implies \sf No: of \ cuboids \ needed = \dfrac{Volume \ of \ cube}{Volume \ of \ a \ cuboid}$

$\implies \dfrac{3375}{45}$

$\implies \underline{\underline{75}}$

$\boxed{\boxed{\bold{75 \ cubes}}}$

                                                                   

Answer 2

Answer:

$\frac{3375}{45} = 75 \: cubes$