Question

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Find the volume, the lateral surface are and the total surface area of the cuboid whose dimensions are:
$\odot$ length = 24 m, breadth = 25 m and height = 6 m

Answer 1

☞︎︎︎ Solution

It is given that length =24 cm, breadth 25 cm=0.25m and height = 6m

We know that

Volume of cuboid =1 ×b× h

By substituting♫︎

★ the value we get :-

Volume of cuboid =24×0.25×6

Lateral surface area of a cuboid

=2(24+0.25)×6

❥︎ On further calculation ♫︎

Lateral surface area of a cuboid =2×24.25×6

By multiplication ✫

Lateral surface area of a cuboid =291 m 2

We know that ︎

Total surface area of cuboid =2(Ib+bh+Ih)

By substituting the value

By substituting the valueTotal surface area of cuboid =2(24×0.25+0.25×6+24×6)

By substituting the valueTotal surface area of cuboid =2(24×0.25+0.25×6+24×6)

On further calculation ☃︎

Total surface area of cuboid =2(6+1.5+144)

Total surface area of cuboid =2(6+1.5+144)

So we get ☀︎︎

Total surface area of cuboid =2×151.5

Total surface area of cuboid =2×151.5By multiplication ☏︎

Total surface area of cuboid =303 sq. cm

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Answer 2

$\bigstar$ Given:-      

• ➻ Length of the cuboid = 24 m
• ➻ Breadth of the cuboid = 25 m
• ➻ Height of the cuboid = 6 m

$\bigstar$ To find:-      

• ➳ The volume of the cuboid
• ➳ The lateral surface area of the cuboid
• ➳ The total surface area of the cuboid

$\bigstar$ Solution:-            

Here, we have given that the length of the cuboid = 24 cm, breadth of the cuboid = 25 cm and height of the cuboid = 6 cm.  

So firstly we will find out the lateral surface of the cuboid by substituting the values in the formula.

✶ The lateral surface area ✶

$\qquad\sf{:\implies\:The\:lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:L\:+\:B\bigg)\:H\:}$

$\qquad\sf{:\implies\:The\:lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:24\:+\:25\bigg)\:6\:}$

$\qquad\sf{:\implies\:The\:lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:49\:\bigg)\:6\:}$

$\qquad\sf{:\implies\:The\:lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:\bigg(\:2\:\times\:49\:\times\:6\:\bigg)}$

$\qquad\sf{:\implies\:The\:lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:\bigg(\:98\:\times\:6\:\bigg)}$

$\qquad\sf{:\implies\:The\:lateral\:surface\:area\:_{(\:CUBOID\:)}\:=\:588\:m^{2}}$

. ° . $\underline{\pmb{The\:lateral\:surface\:area\:of\:the\:cuboid\:is\:588\:m^{2}\:\:.}}$

                      ________________

✶ The total surface area ✶

$\qquad\sf{:\implies\:The\:total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:LB\:+\:BH\:+\:HL\bigg)\:}$

$\qquad\sf{:\implies\:The\:total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:24\:\times\:25\:+\:25\:\times\:6\:+\:6\:\times\:24\bigg)\:}$

$\qquad\sf{:\implies\:The\:total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:600\:+\:150\:+\:144\:\bigg)\:}$

$\qquad\sf{:\implies\:The\:total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:750\:+\:144\:\bigg)\:}$

$\qquad\sf{:\implies\:The\:total\:surface\:area\:_{(\:CUBOID\:)}\:=\:2\:\bigg(\:894\:\bigg)\:}$

$\qquad\sf{:\implies\:The\:total\:surface\:area\:_{(\:CUBOID\:)}\:=\:\bigg(\:2\:\times\:894\:\bigg)}$

$\qquad\sf{:\implies\:The\:total\:surface\:area\:_{(\:CUBOID\:)}\:=\:1788\:m^{2}}$

. ° . $\underline{\pmb{The\:total\:surface\:area\:of\:the\:cuboid\:is\:1788\:m^{2}\:\:.}}$

                    ____________

✶ The volume of the cuboid ✶

$\qquad\sf{:\implies\:The\:volume\:\:_{(\:CUBOID\:)}\:=\:L\:\times\:B\:\times\:H\:}$

$\qquad\sf{:\implies\:The\:volume\:\:_{(\:CUBOID\:)}\:=\:24\:\times\:25\:\times\:6\:}$

$\qquad\sf{:\implies\:The\:volume\:\:_{(\:CUBOID\:)}\:=\:600\:\times\:6\:}$

$\qquad\sf{:\implies\:The\:volume\:\:_{(\:CUBOID\:)}\:=\:3600\:m^{3}}$

. ° . $\underline{\pmb{The\:volume\:of\:the\:cuboid\:is\:3600\:m^{3}\:\:.}}$