how many minimum numbers of wooden cuboids of size 2cm * 3cm * 4cm can make a smallest cube ? cutting is allowed. also find the surface area and volume of cube formed.
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Answered by
6
In this question you use least common multiple:
The least common multiple of 2,3,4
multiples of 2= 2,4,6,8,10,12,14,16......
4=4,8,12,16,20.......
3=3,6,9,12,15,18
Therefore the least common multiple of the 12
Find the dimensions of the cube formed:
For the length = 12÷2 = 6 cm
For the height= 12÷3= 4 cm
For the width = 12÷4 = 3 cm
Hence the dimensions are 6 cm by 4 cm by 3 cm
Volume
length × width ×height
6 × 3 × 4 = 72 cm³
Surface area
2(length x width) + 2(length × height) + 2( width × height)
2(6 × 3) + 2( 6× 4) + 2( 3×4)
(2 × 18) + (2 × 24) + (2 × 12)
36 + 48 + 24
= 108 cm²
The least common multiple of 2,3,4
multiples of 2= 2,4,6,8,10,12,14,16......
4=4,8,12,16,20.......
3=3,6,9,12,15,18
Therefore the least common multiple of the 12
Find the dimensions of the cube formed:
For the length = 12÷2 = 6 cm
For the height= 12÷3= 4 cm
For the width = 12÷4 = 3 cm
Hence the dimensions are 6 cm by 4 cm by 3 cm
Volume
length × width ×height
6 × 3 × 4 = 72 cm³
Surface area
2(length x width) + 2(length × height) + 2( width × height)
2(6 × 3) + 2( 6× 4) + 2( 3×4)
(2 × 18) + (2 × 24) + (2 × 12)
36 + 48 + 24
= 108 cm²
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1
Answer:
The answer is thaeverything is same
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