Question

find the volume, lateral area surface area (LAS) and the total surface area (TSA) of a cuboid whose length 12m,breadth 8m and height 35cm
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Answer 1

What we have to do?

In the above question, Given a cuboid whose length is 12 m , breadth is 8 m and height is 35 cm. We have to find out the Volume, Lateral Surface Area and Total Surface Area.

First we need to convert the given height from centimetres into metres.

To find the Total Surface Area, we will use the Formula :

• ${\boxed{\sf {TSA = 2( Lb + bh + hl )}}}$

Where,

• L = Length of the Cuboid
• B = Breadth of the Cuboid
• H = Height of the Cuboid

To find the Lateral surface area , we will use the formula :

• ${\boxed{\sf {LSA = 2( Length + Breadth ) \times height}}}$

To find the Volume, we will use the formula:

• ${\boxed{\sf {Volume = Length \times breadth \times height}}}$

Now, let's do it :

⠀$\underline{\bf{SoluTion :}}$ ⠀

For Total surface area ,

$\dashrightarrow\:\:\sf TSA = 2( Lb + bh + hl )$

We know ,

• L → 12 m
• B → 8 m
• H → 35 cm or 3.5 m

Putting up the values, we get :

$\dashrightarrow\:\:\sf TSA = 2( 12 \times 8 + 8 \times 3.5 + 3.5 \times 12 )$

$\dashrightarrow\:\:\sf T.S.A = 2 ( 96 + 28.0 + 42.0 )$

$\dashrightarrow\:\:\sf TSA = 2 \times 166$

$\dashrightarrow\:\:\sf TSA = 332 m^{2}$

$:\implies \underline{ \boxed{\sf T.S.A = 332 \: m^{2} }}$

For Lateral surface area :

$:\implies\sf 2( Length + Breadth ) \times height$

Putting up the values, we get :

$:\implies\sf 2 ( 12 + 8 ) \times 3.5$

$:\implies\sf 2 \times 20 \times 3.5$

$:\implies\sf LSA = 140 \: m^{2}$

$\dashrightarrow\:\: \underline{ \boxed{\sf L.S.A = 140 \: m^{2}}}$

For Volume of Cuboid :

$\dashrightarrow\:\:\sf V = Length \times breadth \times height$

Putting up the values, we get :

$\dashrightarrow\:\:\sf V = 12 \times \ 8 \times 3.5$

$\dashrightarrow\:\:\sf V = 336 \: m^{3}$

$:\implies \underline{ \boxed{\sf Volume = 336 \: m^{3}}}$