Question

From a square piece of board of area 144m^2, an open box of square base and 2 m in height is made. find the volume of the box and the area of its walls

Answer 1

Required answer :-

Question:

• From a square piece of board of area 144m^2, an open box of square base and 2 m in height is made. Find the volume of the box and the area of its walls.

Solution:

Given,

• Area of square board = 144cm²

• Height of square board = 2 m

• Breadth of square board = 2 ×2 ×2 =8m

Formulas used:

• Volume of square = Length×Breadth × height

• Area of square = 2( length + breadth) × height

To find:

• Volume of box

• Area of the walls of square

Step by step explaination:

According to the question first we have to calculate the volume of box.

That is,

Volume of square(V) = Length × breadth × height

V = 8m × 8m × 2m

V = 128m³

Now we have to calculate the area of the walls of square

That is,

Area of square(A) = 2 (length + breadth) × height

A = 2 ( 8 + 8 ) × 2

A = 4m × 16m

A = 64m²

Thus volume of box will be 128m³ and area of its wall will be 64m²

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Note:

Refer the attachment as diagram and better understanding.

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Answer 2

Given :-

• A square piece of board of area 144m^2.
• An open box of square base and 2 m in height is made from this board.

To find

• The volume of the box.
• The area of its walls.

Formula Used

$\bigstar \:  \:  \:  \boxed{ \pink{ \:  \rm \: Volume_{(cuboid)} = Length × Breadth × Height }}$

$\bigstar \:  \:  \:  \boxed{ \pink{ \:  \rm \: Area_{(walls)} = 2(Length + Breadth) × Height }}$

$\large\underline\purple{\bold{Solution :- }}$

Here,

Given that

• Area of square sheet = 144 m²

Let side of the square sheet be 'x' meter.

Now, Using formula of area of square, we have

$\bigstar \:  \:  \:  \boxed{ \green{ \:  \rm \: Area_{(square)} = {(side)}^{2} }}$

$\rm :  \implies \: {x}^{2} = 144$

$\rm :  \implies \:\bigstar \:  \:  \:  \boxed{ \pink{ \:  \rm x\: = \: 12 \: m}}$

Now, the square sheet is converted into an open box of height 2 m.

Therefore,

Dimensions of box are as follow:-

• Length of box = 12 - 2 - 2 = 8 m

• Breadth of box = 12 - 2 - 2 = 8 m

• Height of box = 2 m

Now,

• Volume of box is given by

$\rm :  \implies \:Volume_{(cuboid)} = Length × Breadth × Height$

$\rm :  \implies \:Volume_{(cuboid)} =8 \times 8 \times 2$

$\large \boxed{ \pink{\rm :  \implies \:Volume_{(cuboid)} =128 \: {m}^{3} }}$

Also,

• Area of its wall is given by

$\rm :  \implies \:Area_{(walls)} = 2(Length + Breadth) × Height$

$\rm :  \implies \:Area_{(walls)} = \: 2 \times (8 + 8) \times 2$

$\large \boxed{ \blue{\rm :  \implies \:Area_{(walls)} = \: 64 \: {m}^{2} }}$

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More information

Perimeter of rectangle = 2(length× breadth)

Diagonal of rectangle = √(length ²+breadth ²)

Area of square = side²

Perimeter of square = 4× side

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

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