Question

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.​

Answer 1

810 cm^3

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;

`\rm \: Total \; Surface\; area \: of \: the \; cuboid = 2(5z * 3z + 3z * 2z + 2z * 5z`

`\implies \rm \: 279 = 31 {z}^(2)`

• Find z

`\rm \implies {z}^(2) = \cfrac{279}{31}`

`\rm \implies {z}^(2) = 9`

`\implies \rm \: z = √(9)`

`\rm \implies \: z = √(3 * 3) = 3`

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