Question

The length, breadth and height of a cuboid are in the ratio 5:3:2. If its volume is find its dimensions. (Dimensions means: its length, breadth and height). Also find the total surface area of the cuboid.​

Answer 1

Consider length of the given cuboid= 5x

Breadth of the given cuboid=3x

Height of the given cuboid= 2x

We know that,

Volume of the given cuboid =

Length×breadth×height

Substituting the value,

$240cm {}^{3} = 5x \times 3x \times 2x$

$240cm {}^{3} = 30x$

$x {}^{3} = \frac{240}{30} = 8$

So, we get

$x = 8 \frac{1}{3}$

$x = (2 \times 2 \times 2) \frac{1}{3}$

Therefore x→ 2

Length of the given cube = 5x= 5×2→ 10cm

Breadth of the given cube = 3x= 3×2→ 6cm

Height of the given cube = 2x= 2×2→ 4cm

We know that

Total surface area of the given cuboid,

2(l×b+b×h+h×l)

Substituting the values,

2(10×6+6×4+4×10)

2(60+24+40)

2(124)

→248 sq. cm

Answer 2

$\large\underline\mathtt\red{Given:}$

•Ratio of length, breadth and height is 5:3:2

• Volume = $240 cm^3$

$\large\underline\mathtt\blue{To Find:}$

•Length, breadth and height.

•Total surface area.

$\large\underline\mathtt\green{Solution:}$

$\sf{Let\: length \:of\: the\: given\: cuboid\: = 5x}$

$\sf{Breadth \:of\: the\: given\: cuboid\: = 3x}$

$\sf{Height \:of \:the given\: cuboid\: = 2x}$

$\sf{Volume\: of \:the \:given\: cuboid\: = Length}$

$\sf{× Breadth × Height}$

$\sf{= 5x × 3x × 2x = 30x^3}$

$\sf{But \:we \:are \:given \:volume\: = 240 cm^3}$

$\sf{30x^3 = 240 cm^3}$

$\sf{⇒ x^3 = 240/30}$

$\sf{⇒ x^3 = 8}$

$\sf{⇒ x = 8.1/3}$

$\sf{⇒ x = (2 x 2 x 2)^{1/3}}$

$\sf{⇒ x = 2 cm}$

$\sf{Length\: of\: the\: given\: cube\: = 5x = 5 × 2 }$

$\sf{= 10 cm}$

$\sf{Breadth \:of\: the\: given \:cube\: = 3x = 3 × 2 }$

$\sf{= 6 cm}$

$\sf{Height\: of \:the\: given\: cube = 2x = 2 × 2}$

$\sf{= 4cm}$

$\sf{Total\: surface\: area\: of \:the\: given\: cuboid = 2}$

$\sf{(l × b + b × h + h × l)}$

$\sf{= 2(10 × 6 + 6 × 4 + 4 × 10)}$

$\sf{ = 2(60 + 24 + 40) }$

$\sf{= 2 × 124 = 248 cm^2}$