Question

the length breadth and height of a cuboid are in the ratio of 7:5:2 its volume is 35840cmsq.find its dimensions​

Answer 1

Answer:

Step-by-step explanation:

Answer :

The volume of cuboid is 5670 cm³

Step-by-step explanation :

Let the length, breath and height of the cuboid be 7x, 6x and 5x respectively.

According to the question ;

Surface area of cuboid = 1926 cm²

⇒ 2 ( lb + bh + hl ) = 1926

⇒ 2 ( 7x * 6x + 6x * 5x + 5x * 7x ) = 1926

⇒  ( 42 x² + 30 x² + 35x² ) = 1926 / 2

⇒ 107 x² = 963

⇒ x² = 963 / 107

⇒ x² = 9

⇒ x = √9

⇒ x = 3

Therefore, the length, breath and height of the cuboid are ;

Length (l) = 7 * 3 = 21 cm.

Breadth (b) = 6 * 3 = 18 cm.

Height (h) = 5 * 3 = 15 cm.

Volume of cuboid = l × b × h

                             = 21 × 18 × 15

                             = 5670 cm³

Answer 2

ǫᴜᴇsᴛɪᴏɴ-:

The length breadth and height of a cuboid are in the ratio of 7:5:2 its volume is 35840cmsq.find its dimensions

sᴏʟᴜᴛɪᴏɴ-:

★Let the length,breadth and height of the cuboid be 5x , 3x and 2x respectively.

★We know that the volume of the cuboid is $\sf{l \times b\times h}$

★It is given that the volume of the cuboid is $\sf{35.937m^2}$ , therefore.

$\sf{35.937~=~5x \times 3x\times 2x}$

⇝$30x^3$ = $35.937$

⇝$x^3$ = $\frac{35.937}{30}$ = $1.197$

⇝x = $\sqrt{3}{1.197}$

⇝x = $0.33$

★Therefore, the length l = 5x = 5 × 0.33 = 1.65,

★breadth b = 3x = 3 × 0.33 = 0.99 and

★height h = 2x = 2 × 0.33 = 0.66

★Now, the total surface area of cuboid is 2(lb + bh + hl),

therefore, the total surface area with length 1.65 m, breadth 0.99 m and height 0.66 m is:

★A = 2[(1.65×0.99) + (0.99×0.66) + (0.99×1.65)] = 2(1.6335+0.6534+1.089) = 2×3.3759 = $\sf6.7518m^2$

★Hence, the dimensions of cuboid is 1.65 m, 0.99 m and 0.66 m and the total surface area of cuboid is 6.7518 m