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

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;

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

$\implies \rm \: 279 = 31 {z}^{2}$

• Find z

$\rm \implies {z}^{2} = \cfrac{279}{31}$

$\rm \implies {z}^{2} = 9$

$\implies \rm \: z = \sqrt{9}$

$\rm \implies \: z = \sqrt{3 \times 3} = 3$

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