Question

The dimensions of a cuboid are in the ratio 3:2:1 and the total surface area is 4800 square metre . Find its dimensions.
1 point
11.31 m, 22.62 m, 33.94 m
20 m, 80 m, 40 m
20 m , 30 m, 50 m
20 m, 40 m , 60 m ki​

Answer 1

SOLUTION :

Let

• Length(L) =3x m

• Breadth(B)=2x m

• Height(H) =x m

As we know that in a cuboid ,

• $\underline {\boxed {\bf TSA=2(lb+bh+lh)}}$

Substitute the given values :

$\longrightarrow \sf 2 (3x\times2x+2x\times x+3x\times x)=4800$

$\longrightarrow\sf 2 (6x^2+2x^2+3x^2)=4800$

$\longrightarrow\sf 2 (11x^2)=4800$

$\longrightarrow\sf 22x^2=4800$

$\longrightarrow\sf x^2=\cancel{\dfrac {4800}{22}}$

$\longrightarrow\tt x^2 =218.2(Approx)$

$\longrightarrow\sf x=\sqrt {218.2}$

$\longrightarrow\tt x=14.8 (Approx )$

$\to\bf Height =14.8\: m$

$\to\bf Length=3\times14.8=44.4\:m$

$\to\bf Breadth =2x=2\times 14.8=29.6 \:m$