Question

The volume of a cuboid is 420 cubic cm. Find the surface area of ​​the cuboid if its breadth and height are 7 cm and 5 cm respectively.​

Answer 1

$ola$

volume of cuboid =l×b×h=448cm³

=l×b×7=448cm³

=l×b=64cm²

but base is square :

∴l=b

∴l²=64cm²

⇒l=b=8cm

surface area =2(lb+lh+bh)

=2(8×8+8×7+8×7)

=2(64+56+56)

=352cm²

$352cm2$

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Answer 2

Answer:

Given :

Volume of Cuboid = 420 cm³

Breadth of Cuboid = 7 cm

Height of Cuboid = 5 cm

To Find :

Surface Area of Cuboid = ?

Solution :

~ Formula Used :

Volume :

${\orange{\dashrightarrow \: \: {\underbrace{\underline{\purple{\pmb{{ Volume{\small_{(Cuboid)}} = L \times W \times H }}}}}}}}⇢$

Surface Area :

${\orange{\dashrightarrow \: \: {\underbrace{\underline{\purple{\pmb{{ TSA{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}}}}}}⇢$

Where :

➻ L = Length

➻ B = Breadth or Width

➻ H = Height

➻ TSA = Total Surface Area

~ Calculating the Length of Cuboid :

$\begin{gathered} {\longmapsto{\qquad{\sf{ Volume{\small_{(Cuboid)}} = L \times W \times H }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 420 = L \times 7 \times 5 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 420 = L \times 35 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ \cancel\dfrac{420}{35} = L }}}} \\ \\ \ {\qquad{\textsf{ Length of the Cuboid = {\red{\sf{ 12 \: cm }}}}}}\end{gathered}$

~ Calculating the Surface Area :

$\begin{gathered} {:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}} \\ \\ \ {:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2[(12 \times 7) + (7 \times 5) + (5 \times 12)] }}}} \\ \\ \ {:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2(84 + 35 + 60)}}}} \\ \\ \ {:\implies{\qquad{\sf{ TSA{\small_{(Cuboid)}} = 2 \times 179 }}}} \\ \\ \ {\qquad{\textsf{ Surface Area of the Cuboid = {\green{\sf{ 358 \: cm² }}}}}}\end{gathered}$