Question

the dimensions of a Cuboid are in the ratio 4 : 2 : 1 and the total surface area is 2800 m2 find its volume.​

Answer 1

$\sf \: \red \bigstar \: A \: N \: S \: W \: ER$

$\: \:$

$\sf \red \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 8000 { m}^{2}$

$\: \:$

$\sf \red \bigstar \: GIVEN$

➝ RATIO : 4x : 2x : 1x

$\sf \: ➝ \: length = 4x$

$\:$

$\sf \: ➝ \: breadth = 2x$

$\sf \: ➝ \: height = 1x$

$\sf \red \bigstar \: SOLUTION$

$\sf \red{FORMULA \: USED : } \\ \sf{volume \: of \: the \: cuboid = l \times b \times h}$

$\sf \: ➝ = 4x \times 2x \times 1x = 8x ^{3} \: \: \: \: eq \: (1)$

$\sf \red{FORMULA \: USED : } \\ \sf{total \: surface \: area = 2(lb + bh + hl)}$

$\sf \: ➝ = 2(8 {x}^{2} + 2 {x}^{2} + 4 {x}^{2} ) = 16 {x}^{2} + 4 {x}^{2} + 8 {x}^{2}$

$\sf \: 2800 {m}^{2} = 28 {x}^{2}$

$\sf {x}^{2} = \dfrac{2800}{28} = 100$

$\sf \sqrt{100} = x$

$\sf10 = x$

Put the value of x in equation ( 1 )

$\sf \: volume \: = 8(10) ^{3} </strong><strong>$

= 8000 m2

➝ HENCE, THE VOLUME = 8000 m2

Answer 2

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