Question

the length of cuboid is twice its breadth and thrice its height.if the volume is 2304 m^3,find its dimension

Answer 1

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Answer 2

ANSWER
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VOLUME
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The volume is the amount of space that a shape takes up in three dimensions.

VOLUME OF A CUBOID
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Length × Breadth × Height

=> l × b × h cubic units

GIVEN
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VOLUME of the CUBOID = 2304 m³

SOLUTION
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Let the Breadth be b

Lenght = 2b -------------- ( 1 )

Let the Height be h

Lenght = 3h -------------- ( 2 )

From ( 1 ) and ( 2 ) , we get

2b = 3h

=> b = 3h/2

$volume \: = \: l \times b \times h \\ \\ = > 3h \: \times \: \frac{3h}{2} \times h \: = \: 2304 \\ \\ = > \frac{9 {h}^{3} }{2} = 2304 \\ \\ = > 9 {h}^{3} = 2304 \times 2 \\ \\ = > {h}^{3} = \frac{2304 \times 2}{9} \\ \\ = > {h}^{3} = 256 \times 2 = \: 512 \\ \\ = > h = \sqrt[3]{512} \\ \\ = > height = 8 \: m \: \: ans \\ \\ = > length \: = 3 \times 8 = 24 \: m \: \: \: \: ans \\ \\ = > breadth \: = \frac{3 \times 8}{2} = \frac{24}{2} = 12 \: m \: \: \: \: \: \: ans$
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