Question

the length, breadth and height of a cuboid are in the ratio 5:4:2 if the volume of cuboid is 5000 cm,then what will be the surface of the area of the cuboid​

Answer 1

Answer:

  1900 cm²

Step-by-step explanation:

We can use the given ratios and volume to find the scale factor for the dimensions. Knowing the dimensions, we can compute the surface area using the formula for a cuboid.

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dimensions

Let k represent the scale factor. Then the actual dimensions will be 5k, 4k, and 2k. The actual volume will be ...

  V = LWH

  5000 cm³ = (5k)(4k)(2k) = 40k³

  k³ = (5000 cm³)/40 = 125 cm³

  k = ∛(125 cm³) = 5 cm

The cuboid dimensions are 5(5 cm) = 25 cm, 4(5 cm) = 20 cm, and 2(5 cm) = 10 cm.

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area

The surface area of the cuboid can be computed from ...

  A = 2(LW +H(L +W))

  A = 2((25 cm)(20 cm) +(10 cm)(25 +20 cm))

  A = 2(500 cm² +(10 cm)(45 cm)) = 2(950 cm²) = 1900 cm²

The surface area of the cuboid is 1900 cm².