Question

The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.​

Answer 1

Given:

⠀⠀⠀⠀⠀⠀⠀⠀

☞Sum of length, breadth and depth of a cuboid = 19 cm.

☞Length of its diagonal = 11 cm.

⠀⠀⠀⠀⠀⠀⠀⠀

To find:

⠀⠀⠀⠀⠀⠀⠀⠀

Surface area of the cuboid.

⠀⠀⠀⠀⠀⠀⠀⠀

Solution:

⠀⠀⠀⠀⠀⠀⠀⠀

Let the length, breadth and height of the cube be l cm, b cm and h cm respectively. Then,

⠀⠀⠀⠀⠀⠀⠀⠀

l + b + h = 19 cm ------ (1)

⠀⠀⠀⠀⠀⠀⠀⠀

Length of the diagonal is given i.e. 11 cm

⠀⠀⠀⠀⠀⠀⠀⠀

We know that, diagonal of a cuboid =

⠀⠀⠀⠀⠀⠀⠀⠀

$\sqrt{l {}^{2} + b {}^{2} + h {}^{2} }$

$\implies$ l$^{2}$ + b$^{2}$ + h$^{2}$ = 121 ------ (2)

⠀⠀⠀⠀⠀⠀⠀⠀

Now,

⠀⠀⠀⠀⠀⠀⠀⠀

l + b + h = 19

⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ (l$^{2}$ + b$^{2}$ + h$^{2}$) = 121

⠀⠀⠀⠀⠀⠀⠀⠀

l$^{2}$ + b$^{2}$ + h$^{2}$ + 2(lb + bh + lh) = 361

⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ 121 + 2(lb + bh + lh) = 361

⠀⠀⠀⠀⠀⠀⠀⠀

$\implies$ 2(lb + bh + lh) = 240

⠀⠀⠀⠀⠀⠀⠀⠀

Therefore, surface area of the cuboid is 240 cm$^{2}$.

Answer 2

✦ Question :-

The sum of length, breadth and depth of a cuboid is 19 cm and the length of its diagonal is 11 cm. Find the surface area of the cuboid.

Given:

Length + breadth + depth = 19 cm { Cuboid }

Length of diagonal = 11 cm

⠀⠀⠀⠀⠀⠀⠀⠀

To find:

⠀⠀⠀⠀⠀⠀⠀⠀

What is Surface area of the cuboid ?

⠀⠀⠀⠀⠀⠀⠀⠀

Solution:

⠀⠀⠀⠀⠀⠀⠀⠀

We consider the length, breadth and height of the cube be a cm, b cm and c cm .

Then from this we get :-

⠀⠀⠀⠀⠀⠀⠀⠀

a + b + c = 19 cm eqn 1.

⠀⠀⠀⠀⠀⠀⠀⠀

Length of the diagonal = 11 cm

⠀⠀⠀⠀⠀⠀⠀⠀

Diagonal of a cuboid = √ l² + b² + h²

⠀⠀⠀⠀⠀⠀⠀⠀

{ l² + b² + h² = 121 } .....eqn 2

⠀⠀⠀⠀⠀⠀⠀⠀

Then ,

a + b + c = 19

⠀⠀⠀⠀⠀⠀⠀⠀

(l²+ b²+ h²) = 121

⠀⠀⠀⠀⠀⠀⠀⠀

l$^{2}$ + b$^{2}$ + h$^{2}$ + 2(lb + bh + lh) = 361

⠀⠀⠀⠀⠀⠀⠀⠀

121 + 2(lb + bh + lh) = 361

2(lb + bh + lh) = 240

Hence ,

⠀⠀⠀⠀⠀⠀⠀⠀

Surface area of the cuboid is 240 cm².

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .