Question

Find the lateral surface area, the total surface area and volume of the cuboid whose dimensions are: Length= 48cm, breadth= 6dm and height= 1m​

Answer 1

Given :

• Length of Cuboid = 48 cm
• Breadth of Cuboid = 6 cm
• Height of Cuboid = 1 m or 100 cm

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To Find :

• Lateral Surface Area = ?
• Total Surface Area = ?
• Volume = ?

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Solution :

~ We know that :

• Lateral Surface Area :

${\color{pink}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Lateral \; Surface \; Area{\small_{(Cuboid)}} = 2h(l + b) }}}}}$

• Total Surface Area :

${\color{pink}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Total \; Surface \; Area{\small_{(Cuboid)}} = 2(lb + bh + hl) }}}}}$

• Volume :

${\color{pink}{\bigstar}} \: \: {\underline{\boxed{\red{\sf{ Volume{\small_{(Cuboid)}} = l \times w \times h }}}}}$

Where :

• ➙ LSA = Lateral Surface Area
• ➙ TSA = Total Surface Area
• ➙ l = Length
• ➙ w = Width or Breadth
• ➙ h = Height

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~ Calculating the Lateral Surface Area :

$\; \; \longrightarrow \sf \; \; \; { LSA{\small_{(Cuboid)}} = 2h(l + b) }$

$\; \; \longrightarrow \sf \; \; \; { LSA{\small_{(Cuboid)}} = 2 \times 100(48 + 6) }$

$\; \; \longrightarrow \sf \; \; \; { LSA{\small_{(Cuboid)}} = 200(48 + 6) }$

$\; \; \longrightarrow \sf \; \; \; { LSA{\small_{(Cuboid)}} = 200 \times 54 }$

$\qquad \; \; {\pink{:\implies{\underline{\boxed{\green{\sf{ Lateral \; Surface \; Area \; = 10800 \: cm² }}}}}}}$

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~ Calculating the Total Surface Area :

$\; \; \dashrightarrow \sf \; \; \; { TSA{\small_{(Cuboid)}} = 2(lb + bh + hl) }$

$\; \; \dashrightarrow \sf \; \; \; { TSA{\small_{(Cuboid)}} = 2[(48 \times 6) + (6 \times 100) + (100 \times 48)] }$

$\; \; \dashrightarrow \sf \; \; \; { TSA{\small_{(Cuboid)}} = 2(288 + 600 + 4800) }$

$\; \; \dashrightarrow \sf \; \; \; { TSA{\small_{(Cuboid)}} = 2 \times 5688 }$

$\qquad \; \; {\orange{:\implies{\underline{\boxed{\red{\sf{ Total \; Surface \; Area \; = 11376 \: cm² }}}}}}}$

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~ Calculating the Volume :

$\; \; {\longmapsto{\qquad{\sf{ Volume{\small_{(Cuboid)}} = l \times w \times h }}}}$

$\; \; {\longmapsto{\qquad{\sf{ Volume{\small_{(Cuboid)}} =48 \times 6 \times 100 }}}}$

$\; \; {\longmapsto{\qquad{\sf{ Volume{\small_{(Cuboid)}} =48 \times 600 }}}}$

$\qquad \; \; {\color{cyan}{:\implies{\underline{\boxed{\color{darkblue}{\sf{ Volume \; = 28800 \: cm³ }}}}}}}$

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~ Therefore :

❝ Lateral surface Area of the Cuboid is 10800 cm² ,Total Surface Area is 11376 cm² and the volume is 28800 cm³ . ❞

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Answer 2

Answer:

Given Length=48cm, breadth=6dm and height=1m We know that volume of cuboid= length × breadth × height

V = (0.48 × 0.6 × 1)

V = 0.288m3

We know that total surface area of cuboid= 2(l b + b h + h l)

Surface area = 2 (0.48 × 0.6 + 0.6 × 1 + 1 × 0.48) Surface area = 2 (.288 + 0.6 + 0.48)

Total Surface area = 2.736m2

We know that lateral surface area of cuboid= 2 [(l + b) × h]

Lateral surface area = 2 [(0.48 + 0.6) × 1]

Lateral surface area = 2.16 m2

Explaination:

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