pls answer 4) answer
Answers
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