Question

18) The surface area of a cuboid 15 cm long and 12 cm broad is 369 cm^2 . Find the height and volume of the cuboid
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Answer 1

Answer:

• Length of cuboid (l) = 15 cm
• Breadth of cuboid (b) = 12 cm
• Surface Area = 369 cm²
• Find height and volume?

• According to the Question :

⇒ Surface Area = 369 cm²

⇒ 2(lb + bh + hl) = 369

⇒ 2(15*12 + 12*h + h*15) = 369

⇒ 2(180 + 12h + 15h) = 369

⇒ 2(180 + 27h) = 369

⇒ 360 + 54h = 369

⇒ 54h = 369 - 360

⇒ 54h = 9

⇒ h = 9/54

⇒ h = 1/6 cm

∴ Height of the cuboid is 1/6 cm.

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• Volume of the cuboid :

⇢ Volume = Length × Breadth × Height

⇢ Volume = 15 cm × 12 cm × 1/6 cm

⇢ Volume = 15 cm × 2 cm × cm

⇢ Volume = 30 cm³

∴ Hence, Volume of the cuboid is 30 cm³.

Answer 2

Given :

Total surface area of cuboid = 369cm²

Length = 15cm

Breadth = 12cm

To find : Height and Volume

We know that,

total surface area = 2(lb + bh + lh)

let us assume height to be x.

369 = 2[(15×12) + (12×x) + (15×x)]

369 = 2[180 + 12x + 15x]

369 = 2[180 + 27x]

369 = 360 + 54x

369 - 360 = 54x

9 = 54x

$\dfrac{9}{54} = x$

$\dfrac{1}{6} = x$

Verification :

substituting the values :

$369 = 2((15 \times 12) + (12 \times \dfrac{1}{6}) + ( 15 \times \dfrac{1}{6}))$

$369 = 2(180 + 2 + \dfrac{5}{2})$

$369 = 2( \dfrac{360 + 4 + 5}{2})$

$369 = 2(\dfrac{369}{2})$

LHS = RHS

Hence verified

Volume of cuboid = length × breadth × height

$= 15 \times 12 \times \dfrac{1}{6}$

$= 15 \times 2$

Volume = 30cm³

Extras :

Total surface area of cube = 6a²

Volume of cube = a³

Total surface area of cylinder = 2πrh + 2πr²

= 2πr(h+r)

Volume of cuboid = πr²h

[Note : When in the question it's not mentioned whether it's total surface area or lateral surface area, always it should be understood that the question is referring to total surface area]