Question

The dimensions of a cuboid are in a ratio 1:2:3 and it's total surface area is 88m².
Find the volume.

Answer 1

Step-by-step explanation:

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Answer 2

$\underline\mathfrak\pink{Given:-}$

• Dimensions of a cuboid ratio = 1 : 2 : 3
• Total surface area of cuboid is 88m²

$\large\underline\mathfrak{To \: find:-}$

• Find the volume of cuboid ....?

$\large\underline\mathfrak\pink{Solutions:-}$

• Let the length, breadth and height of the cuboid be x, 2x and 3x.

Now,

$\: \: \: \: \: \therefore \: \: Total \: \: surface \: \: area \: \: of \: \: the \: \: cuboid \: \: = \: \: {2} \: {(lb \: + \: {bh} \: + \: {hl})}$

$\: \: \: \: \: \leadsto \: \: {88} \: \: = \: \: {2} \: {(x \: \times \: {2x} \: + \: {2x} \: \times \: {3x} + \: {3x} \: + \: {x})}$

$\: \: \: \: \: \leadsto \: \: {88} \: \: = \: \: {2} \: {({2x}^{2} \: + \: {6x}^{2} + \: {3x}^{2})}$

$\: \: \: \: \: \leadsto \: \: {88} \: \: = \: \: {2} \: {({11x}^{2})}$

$\: \: \: \: \: \leadsto \: \: {88} \: \: = \: \: {22x}^{2}$

$\: \: \: \: \: \leadsto \: \: {x}^{2} \: \: = \: \: \frac{88}{22}$

$\: \: \: \: \: \leadsto \: \: {x}^{2} \: \: = \: \: {4}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {\sqrt{4}}$

$\: \: \: \: \: \leadsto \: \: {x} \: \: = \: \: {2}$

$\: \: \: \: \: Thus, \\ \: \: \therefore \: \: \: Dimensions \: \: of \: \: cuboid$

$\: \: \: \: \: \leadsto \: \: Length \: \: = \: \: x \: \: = \: \: {2} \: {m}$

$\: \: \: \: \: \leadsto \: \: Breadth \: \: = \: \: {2x} \: \: = \: \: {2} \: \times \: {2} \: \: = \: \: {4} \: {m}$

$\: \: \: \: \: \leadsto \: \: Height \: \: = \: \: {3x} \: \: = \: \: {3} \: \times \: {2} \: \: = \: \: {6} \: {m}$

$\: \: \: \: \: \therefore \: \: Volume \: \: of \: \: = \: \: cuboid \: \: = \: \: l \: \times \: b \: \times \: h$

$\: \: \: \: \: \leadsto \: \: {2} \: \times \: {4} \: \times \: {6}$

$\: \: \: \: \: \leadsto \: \: {48}$

$\: \: \: \: \: \: \: \: Hence, \\ \: \: Volume \: \: of \: \: cuboid \: \: {48} \: {m}^{3}.$

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