Question

the length breadth and height of a cuboid are in the ratio 3 ratio 2 ratio 1 and its volume is 6000 cm cube find the total surface area of a cuboid​

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The length, breadth and height of a cuboid are in the ratio 3 : 2 : 1.

• The volume of the cuboid = 6000cm³

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The surface area of the cuboid.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the common ratio of length,breadth and height be x

Length, breadth and height are in the ratio 3 : 2 : 1

Length of cuboid = 3x

Breadth of cuboid = 2x

Height of cuboid = x

As we know that:-

The volume of the cuboid is given by the formula:-

$\boxed{ \rm \leadsto Volume \: of \: cuboid = l \times b \times h}$

Here:-

• l = length = 3x

• b = breadth = 2x

• h = height = x

• Volume = 6000cm³

Therefore:-

${ \rm \implies6000\ = 3x \times 2x \times x}$

${ \rm \implies6000\ = 6 {x}^{3} }$

${ \rm \implies \dfrac{6000}{6}\ = {x}^{3} }$

${ \rm \implies 1000= {x}^{3} }$

${ \rm \implies x = \sqrt[3]{1000} }$

${ \rm \implies x = 10 }$

Length of cuboid

= 3x

= 3 × 10

= 30cm

Breadth of cuboid

= 2x

= 2 × 10

= 20cm

Height of the cuboid

= x

= 10cm

We have:-

Length = 30cm

Breadth = 20cm

Height = 10cm

$\boxed{ \rm Surface \: area \: of \: cuboid = 2(lb + bh + lh)}$

$= 2 \big \{(30 \times 20) + (20 \times 10) + (30 \times 10) \big \}$

$= 2 \big \{(600) + (200) + (300) \big \}$

$= 2 \big \{600 + 200+ 300 \big \}$

$= 2 (1100)$

$=2200$

$\underline{\boxed{ \rm \purple{ \therefore Surface \: area \: of \: cuboid=2200 {cm}^{2} }}}$