Question

Anuj made a cuboid of dough of dimensions 5 cm, 5 cm and 3 cm. How many such cuboids
will he need to make a perfect cube? What will be the dimensions of the cube?

the answer is 45 but I don't know the solution please tell me the solution then I will make you brainlist I'll follow you and I'll like your answer. ​

Answer 1

Answer:

Step-by-step explanation:

The dimensions of the cuboid are:-

Length(l) = 5cm

Breadth(b) = 3cm

Height (h) = 5cm

Let us find the volume of the cuboid formed.

Volume of cuboid = l×b×h

Volume of cuboid = 5×3×5 = 75cm³.

The minimum dimension of the cube will be LCM of dimension of cuboid.

LCM of 5,3,5 = 15.

The  dimension of cube will be 15cm.

$\setlength{\unitlength}{4mm}\begin{picture}(10,6)\thicklines\put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(4.6,-0.5){\bf\large 15cm}\put(13.5,3){\bf\large 15cm}\put(-4,5.8){\bf\large15 cm}\end{picture}$

Now , we have to find the volume of the cube.

Volume = a³

Volume = (15cm)³ = 3375 cm³.

Therefore, the number of cubes required to make the cuboid will be =

Volume of Cube        

Volume of cuboid

$\implies$ $\dfrac{3375}{75}$

So, the number of cuboids needed = 45.