The cuboids of dimension 15cm × 9cm × 4cm are cut from a cube of wood of least possible length such that no part of wood is wasted.
How many such cuboids can be cut from the cube?
a) 1080
b) 3240
c) 10800
d) 32400
Answers
Given :
- We have cube of wood, from it cuboid are cut
- Dimensions of cuboid = 15cm × 9cm × 4cm
- No part of wood is wasted
To find :
Number of cuboid
Formula used :
- Volume of cube = side³
- Volume of cuboid = length × breadth × height
Solution :
Let side of cube = x
Now we know that cuboid is cut such that no part is wasted,
This means that x can be divided into 15cm , 9cm and 4cm without leaving a reminder.
Therefore, from above we get that , x is LCM of 15,9 and 4
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LCM of 15 , 9 and 4
15 = 3 × 5
9 = 3×3
4 = 2×2
Therefore, LCM = 3×5×3×2×2 = 180
Therefore, side of cube = x = 180cm
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Volume of cube = (180 cm)³
➝ Volume of cube = 5,832,000 cm³
Volume of cuboid = 15cm × 9cm × 4cm
➝ Volume of cuboid = 540 cm³
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Let , number of cuboid cut = y
Therefore, Volume of cube = Number of cuboid × volume of one cuboid
➝ 5,832,000 = y × 540
➝ y = 5,832,000 ÷ 540
➝ y = 10,800
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ANSWER :
Option c) Number of cuboid cut = 10800