Question

The length , breadth and height of a cuboid are in the ratio 3:2:1. If its volume is 162
cm³ , find its total surface area.



please answer these question fast tomorrow is my exam​

Answer 1

Answer:

correct answer is 198cm^2

Answer 2

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The length , breadth and height of a cuboid are in the ratio 3:2:1. If its volume is 162

cm³ , find its total surface area.

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T.S.A of Cuboid is 198cm³

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• Ratio of dimensions of cuboid is 3:2:1
• Volume of Cuboid = 162 cm³

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• T.S.A of Cuboid = ?

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$\bf Volume \: of \: Cuboid =l \times b \times h$

$\bf T.S.A \: of \: Cuboid = 2(lb \times bh \times hl)$

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

$\bf Volume \: of \: Cuboid =162 {cm}^{2}$

$\bf \implies l \times b \times h = 162$

$\bf \implies 3x \times 2x \times x = 162$

$\bf \implies {6x}^{3} = 162$

$\bf \implies {x}^{3} = 162 \div 6$

$\bf \implies {x}^{3} = 27$

$\bf \implies x = \sqrt[3]{27}$

$\bf \implies x = 3cm$

$\bf T.S.A \: of \: Cuboid = 2(lb \times bh \times hl)$

$\bf = 2(9 \times 6 + 6 \times 3 + 3 \times 9)$

$\bf = 2(54 + 18 + 27)$

$\bf = 2 \times 99$

$\bf = 198 {cm}^{3}$

Therefore, T.S.A of Cuboid is 198cm³.

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