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A wall 9 m long, 6 m high and 20 cm thick, is to be constructed using bricks of dimensions 30 cm, 15 cm and 10 cm. The number of bricks required will be 2400.

A.True

B.False

Answer
Verified

Hint: Volume represents the capacity of any solid. Volume of any cuboid with length as ‘l’, breadth as ‘b’ and height as ‘h’ can be given as \[=l\times b\times h\]. Get volumes of brick and wall using the given dimensions. Calculate the total volume of the wall using the volume of brick and number of the wall using the wall using the volume of brick and number of bricks involved to construct the wall.

Now, equate them to get the value of bricks as both represent the same volume of a solid.

__Complete step-by-step answer:__

We know that wall brick will be of the cuboid shape and the wall is constructed using the bricks. It means the volume of the total number of bricks involved to construct the wall should be equal to the volume of the wall because volume represents capacity of any solid within itself.

Let there be ‘n’ bricks involved to construct the wall of a given dimension.

So, we know the volume of any cuboid with given measurement as

Volume of cuboid \[=length\times breadth\times height\] ……………………………….(i)

Now, we have dimension of wall as

Length \[=9m\]

Height \[=6m\]

Breadth (thickness) \[=20cm\]

Now, we know

\[1m=100cm\]

Hence, length of the wall in cm can be given as

Length \[9m=9\times 100cm=900cm\]

Similarly, height can be given as

\[6m=6\times 100cm=600cm\]

Volume of the wall can be given as

Volume of the wall \[=900\times 600\times 20c{{m}^{3}}\] ………………………..(ii)

Now, we can get volume for brick using equation (i)

So, dimensions of a brick are given as \[\left( 30cm,15cm,10cm \right)\].

Hence, volume of a brick can be calculated as

Volume of a brick $=30\times 15\times 10c{{m}^{3}}$ …..................................(iii)

Now, we have already supposed that ‘n’ bricks are involved for making the wall of given dimensions.

So, the volume of n bricks can be calculated by multiplying ‘n ‘ by the volume of one brick from the equation (iii). Hence, we get

Volume of n bricks $=n\times 30\times 15\times 10c{{m}^{3}}$ …………………………………..(iv)

Now, we know that ’n’ bricks are involved to make the wall, hence volume of both of them should be equal as n bricks are occupying the spaces of the wall.

Hence, from equation(ii) and (iv), we get

$900\times 600\times 20=n\times 30\times 15\times 10$

$n=\dfrac{900\times 600\times 20}{30\times 15\times 10}$

$n=30\times 40\times 2$

$n=2400$

Hence, the given statement is true that the number of bricks required to make a wall of given dimensions by a brick with the provided dimension are 2400.$=n=2400$

Hence, option (A) is correct.

Note: Equating volume of both the rectangular cuboids (bricks and wall) is the key point of the question. One may get confused and he/she tries to equate the surface areas of both of them which is the wrong approach as the surface area of the bricks and wall are not equal as Area does not represent the capacity of any solid.

Conversion of units of any dimension is the key point of the question as well. Try to use ‘cm’ or ‘m’ for representing the dimension, i.e. use only one unit for these kinds of questions.

Now, equate them to get the value of bricks as both represent the same volume of a solid.

We know that wall brick will be of the cuboid shape and the wall is constructed using the bricks. It means the volume of the total number of bricks involved to construct the wall should be equal to the volume of the wall because volume represents capacity of any solid within itself.

Let there be ‘n’ bricks involved to construct the wall of a given dimension.

So, we know the volume of any cuboid with given measurement as

Volume of cuboid \[=length\times breadth\times height\] ……………………………….(i)

Now, we have dimension of wall as

Length \[=9m\]

Height \[=6m\]

Breadth (thickness) \[=20cm\]

Now, we know

\[1m=100cm\]

Hence, length of the wall in cm can be given as

Length \[9m=9\times 100cm=900cm\]

Similarly, height can be given as

\[6m=6\times 100cm=600cm\]

Volume of the wall can be given as

Volume of the wall \[=900\times 600\times 20c{{m}^{3}}\] ………………………..(ii)

Now, we can get volume for brick using equation (i)

So, dimensions of a brick are given as \[\left( 30cm,15cm,10cm \right)\].

Hence, volume of a brick can be calculated as

Volume of a brick $=30\times 15\times 10c{{m}^{3}}$ …..................................(iii)

Now, we have already supposed that ‘n’ bricks are involved for making the wall of given dimensions.

So, the volume of n bricks can be calculated by multiplying ‘n ‘ by the volume of one brick from the equation (iii). Hence, we get

Volume of n bricks $=n\times 30\times 15\times 10c{{m}^{3}}$ …………………………………..(iv)

Now, we know that ’n’ bricks are involved to make the wall, hence volume of both of them should be equal as n bricks are occupying the spaces of the wall.

Hence, from equation(ii) and (iv), we get

$900\times 600\times 20=n\times 30\times 15\times 10$

$n=\dfrac{900\times 600\times 20}{30\times 15\times 10}$

$n=30\times 40\times 2$

$n=2400$

Hence, the given statement is true that the number of bricks required to make a wall of given dimensions by a brick with the provided dimension are 2400.$=n=2400$

Hence, option (A) is correct.

Note: Equating volume of both the rectangular cuboids (bricks and wall) is the key point of the question. One may get confused and he/she tries to equate the surface areas of both of them which is the wrong approach as the surface area of the bricks and wall are not equal as Area does not represent the capacity of any solid.

Conversion of units of any dimension is the key point of the question as well. Try to use ‘cm’ or ‘m’ for representing the dimension, i.e. use only one unit for these kinds of questions.

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