Question

A cuboidal tin box opened at the top has dimensions 20 cm × 16 cm× 14 cm. What is the total area of metal sheet required to make such a box? Also, find it's volume.

Answer 1

$\large\underline{\sf{Solution-}}$

Given that,

A cuboidal tin box opened at the top has dimensions 20 cm × 16 cm× 14 cm.

It means,

Length of cuboidal box = 20 cm

Breadth of cuboidal box = 16 cm

Height of cuboidal box = 14 cm

Now,

The area of metal sheet required to make the open cuboidal box = Curved Surface Area of Cuboid + Area of base

$\rm \: = \:2(length + breadth) \times height + length \times breadth$

$\rm \: = \:2(20 + 16) \times 14 + 20 \times 16$

$\rm \: = \:(36) \times 28 + 320$

$\rm \: = \:1008 + 320$

$\rm \: = \:1328 \: {cm}^{2}$

Now, Volume of box is

$\rm \: = \:length \times breadth \times height$

$\rm \: = \:20 \times 16 \times 14$

$\rm \: = \:320 \times 14$

$\rm \: = \:4480 \: {cm}^{3}$

Hence,

$\rm \: Area \: of \: metal \: sheet \: used \: = \: 1328 \: {cm}^{2}$

and

$\rm \: Volume \: of \: box \: = \: 4480 \: {cm}^{3}$

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Additional Information

Formulae of Cube :-

Total Surface Area = 6(side)²

Curved Surface Area = 4(side)²

Volume of Cube = (side)³

Diagonal of a cube = √3(side)

Perimeter of cube = 12 x side

Formulae of Cuboid

Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

Curved Surface area = 2 height(length + breadth)

Volume of the cuboid = (length × breadth × height)

Diagonal of the cuboid =√(l² + b² + h²)

Perimeter of cuboid = 4 (length + breadth + height)

Answer 2

Step-by-step explanation:

Length of the cuboidal box (l)=20 cm

Breadth of the cuboidal box (b)=16 cm

Height of the cuboidal box (h)=14 cm

Since, box is opened at the top

∴ Area of the metal sheet required to make 1 box

$\pmb{\[ \begin{array}{l} \tt =2 h(l+b)+(l \times b) \\ \tt = 2 \times 14(20+16)+(20 \times 16) \\ \tt = 28 \times 36+320 \\ \tt =1008+320=1328 cm ^{2} . \end{array} \]}$

Volume = l×b×h

= 20×16×14

= 320×14

= 4,480 cm³