Question

The length, breadth and height of a
cuboid are in the ratio 3:4:6 and
its volume is 576 cm3. The whole
surface area (in cm?) of the cuboid
is

Answer 1

★ Given :

• The length, breadth and height of a cuboid are in the ratio 3:4:6.
• Volume is 576 cm³.

★ To find :

• whole surface area (in cm) of the cuboid is ?

★ Solution :

Let Length (l) = 3x, Breadth (b) = 4x, Height (h) = 6x

3x × 4x × 6x = 576

x³ = 576 / 3 × 4 × 6

x³ = 576 / 72

x³ = 8

x = ³√8 = 2 cm

∴ Length = 3 × 2 = 6 cm

Breadth = 4 × 2 = 8 cm

Height = 6 × 2 = 12 cm

◆ Now, we know that :-

Total surface area (TSA) = 2 ( lb + bh + hl )

= 2 ( 6 × 8 + 8 × 12 + 12 × 6 )

= 2 ( 48 + 96 + 72 )

= 2 ( 216 )

= 432 cm²

Hence, The whole surface area of the cuboid is 432 cm²

Answer 2

$\Large\color{pink}{\bigstar}\color{blue}{\mathtt{Question :}}$

➙ The length, breadth and height of a

cuboid are in the ratio 3:4:6 and

its volume is 576 cm3. The whole

surface area (in cm?) of the cuboid

is .

$\Large\color{pink}{\bigstar}\color{blue}{\mathtt{Answer :}}$

➙ Given that ,

$\boxed{\mathtt{\pink{L:B:H=3:4:6}}}$

➙ We know ,

$\boxed{\mathtt{\pink{volume=L×B×H}}}$

᠉ 576 = 3x × 4x × 6x

᠉ 72x³ = 576

᠉ x³ = $\bf{\cancel{\frac{576}{72}}}$

᠉ x³ = 8

᠉ x = $\bf\sqrt[3]{8}$

᠉ x = 2

$\:$

➙ $\boxed{\mathtt{\pink{L=3x=6}}}$

➙$\boxed{\mathtt{\pink{B=4x=8}}}$

➙$\boxed{\mathtt{\pink{H= 6x=12}}}$

$\therefore$ L = 6cm , B = 8cm , H = 12cm .

$\:$

$\boxed{\mathtt{\pink{Total\: surface\: area\:=\: 2(LB+BH+HL}}}$

᠉ 2 ( 6 × 8 + 12 × 8 + 12 × 6 )

᠉ 2 ( 48 + 96 + 72 )

᠉ 432cm²

➙$\boxed{\mathtt{\pink{Total\: surface\: area\:=\: 432cm²}}}$

$\:$

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