Question

2. If the length
, breadth and height of a cuboid are in the ratio 6 : 5: 4 and the total surface area of
the cuboid is 33300 cm2, then the breadth of the cuboid is
(a) 85 cm
(b) 75 cm
(d) cannot be determined
(c) 65 cm
​

Answer 1

Answer:

Option (b) is correct. Breadth of cuboid is 75 cm.

Step-by-step explanation:

Given that,

Length, breadth and height of cuboid are in ratio 6:5:4.

Total surface area of cuboid is 33300 cm².

Let,

Length, breadth and height of cuboid be 6x, 5x and 4x.

We know,

Total surface area of cuboid = 2(lb + bh + lh)

[l is length, b is breadth and h is height of cuboid]

Put values :

$\longrightarrow$ 33300 = 2×[(6x × 5x)+(5x × 4x)+(6x × 4x)]

$\longrightarrow$ 33300 = 2 × (30x² + 20x² + 24x²)

$\longrightarrow$ 33300 = 60x² + 40x² + 48x²

$\longrightarrow$ 33300 = 148x²

$\longrightarrow$ 33300/148 = x²

$\longrightarrow$ 225 = x²

$\longrightarrow$ x =√225

$\longrightarrow \pmb{\sf x = 15}$

So,

Length = 6x = 6×15 = 90

Breadth = 5x = 5×15 = 75

Height = 4x = 4×15 = 60

Therefore,

Breadth of cuboid is 75 cm.

Answer 2

Given : The length, breadth and height of a cuboid are in the ratio 6 : 5: 4 & Total surface area of the cuboid is 33300 cm²

Need To Find : Breadth of Cuboid .

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

❍ Let's Consider the Length, Breadth & Height of Cuboid be 6x , 5x & 4x respectively.

$\dag\frak{\underline { As,\:We\:know\:that\::}}$

$\star\boxed {\pink{ \small {\sf{ Total \:Surface \:Area\:_{(Cuboid)} = 2 ( lb + bh + lh ) }}}}$

Where,

• l is the Length of Cuboid, b is the Breadth of Cuboid & h is the Height of Cuboid.

$\underline {\frak{\star\:Now \: By \: Substituting \: the \: known\: Values \::}}$

$\qquad:\implies \sf{ 33300 = 2 \bigg( ( 6x \times 5x ) + (5x \times 4x ) + ( 6x \times 4x )\bigg) }$

$\qquad:\implies \sf{ 33300 = 2 \bigg( 30x^{2} + 20x^{2} + 24x^{2} \bigg) }$

$\qquad:\implies \sf{ 33300 = 60x^{2} + 40x^{2} + 48x^{2} }$

$\qquad:\implies \sf{ 33300 = 148x^{2} }$

$\qquad:\implies \sf{ \cancel {\dfrac{33300}{148}} = x^{2} }$

$\qquad:\implies \sf{ 225 = x ^{2} }$

$\qquad:\implies \sf{ \sqrt{225} = x^{2} }$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm { x = 15\: cm}}}}\:\bf{\bigstar}$

Therefore,

• Length of Cuboid is 6x = 6 × 15 = 90 cm .

• Breadth of Cuboid is 5x = 5 × 15 = 75 cm

• Height of Cuboid is 4x = 4 × 15 = 60 cm .

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm { Hence , \:  Breadth \:of\:Cuboid \:is\:\bf{75\: cm}}}}$

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