Question

pls answer 4) answer​

Answer 1

Step-by-step explanation:

Given:-

Debnath has made a cuboid whose length , breadth and height are 4 cm , 3 cm and 2 cm respectively.

To find:-

How many cuboids of this type will form a cube .

Solution:-

Length of the cuboid (l) = 4 cm

Breadth of the cuboid (b)= 3 cm

Height of the cuboid (h) = 2 cm

Volume of a cuboid = lbh cubic units

Volume of the given cuboid =

4×3×2

=>24 cubic cm

Volume of the given cuboid = 24 cubic cm----(1)

Let the required number of cuboids be "n"

then

cuboids of this type will form a cube so

The length of the edge of the cube is the LCM of the measurements of the cuboid

LCM of 4,3,2 is 12

So length of the edge = 12 cm

Volume of a cube of a side "a" units = a^3 cubic units

Volume of the cube

= 12^3 cubic cm

=>12×12×12 cubic cm

=>1728 cubic cm

Volume of the cube = 1728 cubic cm ------(2)

Number of cuboids × Volume of each cuboid = Volume of a cube

From (1)&(2)

=>n× 24 = 1728

=>n = 1728/24

=>n= 72

Number of cuboids = 72

Answer:-

Required number of cuboids of the given type to form a cube = 72

Used formulae:-

• Volume of a cuboid = lbh cubic units
• Volume of a cube of a side "a" units = a^3 cubic units