5. Rahul makes a cuboid of plasticine of sides 3 cm x 3 cm x 5 cm. How many such cuboids will he need to form a cube? why have taken the LCM of 3 cm x 3 cm x 5 cm?
Answers
Step-by-step explanation:
We know that a cube will have equal sides
That is if the length of one side is ‘A’
Then its dimensions are A*A*A
Now we need to make a cube using 3*3*5 cuboids
Since from the dimensions of the cuboid we have two different numbers, they are 3 and 5
Now we need to find a least number which is a multiple of both numbers, for this we can multiply thise numbers so that we can get the least number which is a multiple of those two
3*5=15
Now imagine int the following way
1) Keep one the 3*3 faces in front of you, now the side of length 5 is perpendicular to your body surface
2) Now clone up this cuboid one upon one so that the resultant height becomes 15, since we are stacking cuboids of dimensions 3*3*5 one upon one keeping 3*3 on your face, the resultant height will be a multiple of 3
=>n(1)*3=15
=>n(1)=5
So you need to clone the cuboid vertically 5 times.
3) Now the resulting 3d figure will be of dimensions 15*3*5, we got one side equal to 15,
Now we need to get the other two sides equal to 15
4) For the second side, keeping 15*3 face in front of you clone it horizontally in a direction away from you, if you do this the length 5 will increase in multiples of 5,clone it till u get it equal to 15
=>n(2)*5=15
=>n(2)=3
So you need to clone it 3 times in your opposite direction
5) Now you will be left with a new 3d figure of dimensions 15*3*15,
Now clone this whole set so that 3’s will add up to become 15,
=>n(3)*3=15
=>n(3)=5
You need to clone it 5 times in the horizontal plane in the other direction leaving your opposite direction.
Now you will get a cube of dimensions 15*15*15
6) Now how many times you cloned a single cuboid is
=> n(1)*n(2)*n(3) = 5*3*5 = 15*3 = 75
So you need 75 cuboids to make a cube.