Question

A cuboidal box has height, lengthand width as 20 cm, 15 cm and 10cm respectively. Find its total surfacearea and volume.​​

Answer 1

The total surface area of the cuboid is 1300 cm² . The length,breadth and height of a cuboid are 20cm ,15cm ,10cm respectively. Therefore the total surface area of the cuboid is 1300 cm²

Answer 2

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

Given that,

↝ Height of cuboidal box, h = 20 cm

↝ Length of cuboidal box, l = 15 cm

↝ Breadth of cuboidal box, b = 10 cm

We know,

Volume of the Cuboid is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: Volume_{Cuboid} \: = \: l \: \times \: b \: \times \: h \: }}}$

Where,

• l is the length of cuboid

• b is the breadth of cuboid

• h is the height of cuboid

So, on substituting the values, we get

$\rm :\longmapsto\:Volume_{Cuboid} = 20 \times 15 \times 10$

$\rm \implies\:\boxed{ \tt{ \: Volume_{Cuboid} \: = \: 3000 \: {cm}^{3} \: }}$

Also, We know

Total Surface Area of Cuboid is

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: TSA_{cuboid} = 2(l \times b + b \times h + h \times l) \: }}}$

Where,

• l is the length of cuboid

• b is the breadth of cuboid

• h is the height of cuboid

So,

On substituting the values, we get

$\rm :\longmapsto\:TSA_{cuboid}$

$\rm \: = \: 2(15 \times 10 + 10 \times 20 + 20 \times 15)$

$\rm \: = \: 2(150+ 200 + 300)$

$\rm \: = \: 2(650)$

$\rm \: = \:1300 \: {cm}^{2}$

Hence,

$\rm \implies\:\boxed{ \tt{ \: TSA_{cuboid} \: = \: 1300 \: {cm}^{2} \: }}$

Thus,

$\begin{gathered}\begin{gathered}\bf\: \rm \implies\:\begin{cases} &\sf{Volume_{Cuboid} = 3000 \: {cm}^{3} } \\ \\ &\sf{TSA_{cuboid} = 1300 \: {cm}^{2} } \end{cases}\end{gathered}\end{gathered}$

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Additional Information

↝ Formula's 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

↝ Formula's 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)

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

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