5. How many cuboids of dimensions 15cm 30cm,15cm will be needed to forma cube?
(a) 15
(b) 4
(c) 30
(d) 5
Answers
Option (b)
Step-by-step explanation:
Given :-
Cuboid of dimensions 15cm 30cm,15cm
To find :-
How many cuboids of dimensions 15cm 30cm,15cm will be needed to form a cube?
Solution :-
Given that :
Dimensions of a cuboid = 15cm 30cm,15cm
Length of the cuboid (l) = 15 cm
Breadth of the cuboid (b) = 30 cm
Height of the cuboid (h) = 15 cm
15= 15×1
30 = 15×2
15=15×1
LCM of 15 , 30 ,15 = 30
So the dimensions can be written as
15×2 = 30
30×1 = 30
15×2 = 30
A cuboid has all sides equal then It is a cube
So , the edge of the cube should be
30 cm
The number of cuboids to required to form a cube
=>2×1×2
=> 4
So 4 cuboids are required.
Answer:-
4 cuboids are required to form a cube of 30 cm.
Check:-
Cuboid of dimensions 15cm 30cm,15cm
Volume of a cuboid = lbh cubic units
Volume of the given cuboid = 6750 cm³
Let the required number of cuboid be "n" to form a cube
Total volume of "n" cuboids = 6750n cm³----(1)
Edge of a cube = 30cm
Volume of the cube = 30³ cm³
=> 27000 cm³----------(2)
we know that
If one solid is converted to another solid then the volume of both solids are same.
=> Volume of a cube = volume of n cuboids
=>(1) = (2)
=> 27000 = 6750n
=>n = 27000/6750
=>n = 4
Number of cuboids = 4
Verified the given relations in the given problem.
Used formulae:-
- Volume of a cuboid = lbh cubic units
- Volume of a cube = a³ cubic units
- If one solid is converted to another solid then the volume of both solids are same.
- Where, l = length of the cuboid
- b= breadth of the cuboid
- h = height of the cuboid
- a = Edge of the cube