Question

A closed box of dimensions 40 cm x 20 cm x 5 cm is made from a sheet of metal. How much sheet of metal is required?
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Answer 1

$\Large{\underbrace{\sf{\orange{Required\:Answer:}}}}$

Given :

• The dimensions of α closed box αre 40cm×20cm×5cm.

To Find :

• Metαl sheet required to cover this closed box.

Required Knowledge :

$\large\star{\boxed{\sf{\orange{T.S.A_{(cuboid)} = 2(lb+bh+hl)}}}}$

Solution :

• Substitute the vαlues in the formulαe of T.S.A (Totαl Surfαce Areα) of cuboid.

$\longrightarrow{\sf{ 2\big[ (40cm\times 20cm) + (20cm\times 5cm) + (5cm\times 40cm)\big]}}$

• Solve the brackets first.

$\longrightarrow{\sf{ 2( 800cm^{2} + 100cm^{2} + 200cm^{2})}}$

• Add the numbers inside the brαcket.

$\longrightarrow{\sf{ 2(1100cm^{2})}}$

• Multiply this.

$\longrightarrow{\boxed{\sf{\red{ 2200cm^{2}}}}}$

Hence, the metαl sheet required to cover the closed box is 2200cm².

And we αre done! :)

__________________________

Answer 2

Dimension of the box = 40 cm × 20 cm × 5 cm

We know, $TSA_{cuboid} = 2(lb + bh + lh)$.

∴ Quantity of metal required to make the box:-

$2(40 \times 20 + 20 \times 5 + 5 \times 40)$ cm²

= $2(800 + 100 + 200)$ cm²

= $2(1100)$ cm²

= $2200$ cm² or $0.22$ m².

Thus, 0.22 m² sheet of metal is required to construct the box.

More about cuboids:-

• All faces of a cuboid are rectangles. Moreover, it is a 3D object, i.e., has height, breadth and length.
• LSA of cuboid = $2h(l + b)$.
• Volume of cuboid = $(lbh)$.
• Volume of a hollow cuboid = $(l'b'h' - lbh)$.
• Diagonal of cuboid = $\sqrt{l^2 + b^2 + h^2}$.