contestada

The length, breadth and height of a cuboid bear the ratio 5:3:2 . If it's total surface area is 279 cm²,find it's volume.​

Respuesta :

Itz5151

Answer:

810 cm^3

Step-by-step explanation:

Since,the l(length) b(breadth) & h(height) of the cuboid bear the ratio 5 : 3 : 2 ,we could assume it as:

  • l = 5z
  • b = 3z
  • h = 2z

We know that,

  • Cuboid ( total surface area)= 2lb+2lh+2hb cubic units

So substitute the dimensions we assumed:

  • We could write it as;

[tex] \rm \: Total \; Surface\; area \: of \: the \; cuboid = 2(5z \times 3z + 3z \times 2z + 2z \times 5z[/tex]

[tex] \implies \rm \: 279 = 31 {z}^{2} [/tex]

  • Find z

[tex] \rm \implies {z}^{2} = \cfrac{279}{31} [/tex]

[tex] \rm \implies {z}^{2} = 9[/tex]

[tex] \implies \rm \: z = \sqrt{9} [/tex]

[tex] \rm \implies \: z = \sqrt{3 \times 3} = 3[/tex]

Hence, according to the formula,

  • Cuboid V = lbh

We got the dimensions of the cuboid, i.e.

Then, solve.

  • Cuboid V = lbh
  • 15 cm * 9 cm * 6 cm
  • 810 cm^3

Hence,the volume of the cuboid will be 810 cm^3

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