Question

The edges of a cuboid are in the ratio 1:2:3 and its surface area is 88 cm cuboid the volume if the cuboid

Answer 1

$\huge\textbf{Solution}$

$\textbf{Ratio of edges of cuboid = 1 : 2 : 3}$

$\mathbf{Let, l = x, b = 2x, h = 3x }$

$\boxed{Surface \: area =88c {m}^{2}}$

$\boxed{2( lb + bh + hl) = 88}$

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

$2(11 {x}^{2} ) = 88 \\ \\ 22 {x}^{2} = 88 \\ \\ {x}^{2} = \frac{88}{22} \\ \\ {x}^{2} = 4 \\ \\ x = \sqrt{2 \times 2} \\ \\ x = 2$

∴l=2cm , b=4cm, h=6cm

∴ Volume = lbh cubic.unit

=(2×4×6)cm^3

$\huge\boxed{\bold{=48cm^3}}$

Thanks

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