Question

the ratio of length breadth height of a solid cube is 3:2:1 and the total surface area is 750sq cm.calculate it's volume.​

Answer 1

Given :-

Ratio of length breadth height of a solid cube is 3:2:1

Surface area = 750 sq.cm

Explanation :-

Let length , breadth and height of a solid cube be 3x , 2x and x.

Then,

Total Surface area =

$➛ \: 2 \: (lb \: + bh + hl)$

So , Surface area = 750 sq. cm

$750 \: = 2 \: (3x.2x \: + 2x.x \: + x.3x)$

$750 \: = 2 \: (6 {x}^{2} + 2 {x}^{2} + 3 {x}^{2} )$

$750 \: = 2 \times 11 {x}^{2}$

$750 \: = \: 22 {x}^{2}$

${x}^{2} \: = \frac{750}{22}$

${x}^{2} = 34.0909$

$x \: = 5.838$

So , length = 3x = 3 × 5.838 = 17.5 cm

Breadth = 2x = 2 × 5.838 = 11.68 cm

height = x = 5.838 cm

So , Volume = l × b × h

Volume = 17.5 × 11.68 × 5.838

Volume = 1193.28 cube. cm

So , volume = 1193 cm^3

_________________________

Answer 2

Given :  ratio of length breadth height of a solid cuboid is 3:2:1

Correction in Question : ( cube should be cuboid ) and volume given

Volume of cube = 750 cm³

To Find : Surface area of cube

Solution:

length breadth height of a solid cuboid  is 3:2:1

Let say the sides are 3x , 2x and x  cm

Volume = 3x * 2x * x = 6x³

6x³ = 750

=> x³ = 125

=> x = 5 cm

3x  = 3 (5) = 15 cm

2x = 2(5) = 10 cm

x  = 5 cm

Surface area = 2( 15 * 10  + 15 * 5 + 10 * 5)

= 2( 150 + 75 + 50)

= 2 (275)

= 550 cm²

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