Question

Find the difference between the total surface area and the lateral surface area of a cuboid of length 2 m, breadth 1.5 m and height 1 m.​

Answer 1

$\large\sf\underline{Understanding\:the\:question:}$

Here in this question we are given length as 2m , breadth as 1.5 m and height as 1 m of a cuboid . We need to find the difference between total surface area and the lateral surface area of the cuboid . So firstly we need to find the Total surface area and then Lateral surface area of the cuboid . We will use some formula and solve this question . So let's begin !

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$\large\sf\underline{Given\::}$

• Length = 2 m

• Breadth = 1.5 m

• Height = 1 m

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$\large\sf\underline{To\:find\::}$

• Difference between Total surface area and the lateral surface area.

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$\large\sf\underline{Solution\::}$

We know ,

$\small\fbox\red{Total\:surface\:area\:=\:2(lb+bh+hl)}$

• Substituting the value of l , b and h in the formula

$\sf\implies\:TSA\:=\:2(2 \times 1.5 + 1.5 \times 1 + 1 \times 2)$

$\sf\implies\:TSA\:=\:2(3 + 1.5 + 2)$

$\sf\implies\:TSA\:=\:2(3 + \frac{15}{10} + 2)$

$\sf\implies\:TSA\:=\:2(\frac{30+15+20}{10})$

$\sf\implies\:TSA\:=\:2(\frac{65}{10})$

$\sf\implies\:TSA\:=\:2 \times 6.5$

$\large{\mathfrak\blue{\implies\:TSA\:=\:13\:m^{2}}}$

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Also we know that ,

$\small\fbox\red{Lateral\:surface\:area\:=\:2(l+b)h}$

• Substituting the value of l , b and h in the formula

$\sf\implies\:LSA\:=\:2(2 \times 1.5) 1$

$\sf\implies\:LSA\:=\:2(3)1$

$\sf\implies\:LSA\:=\:2 \times 3 \times 1$

$\sf\implies\:LSA\:=\:6 \times 1$

$\large{\mathfrak\blue{\implies\:LSA\:=\:6\:m^{2}}}$

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Now let's find the difference between total surface area and lateral surface area :

$\sf\:TSA-LSA$

• Substituting the value of TSA and LSA we got

$\sf\implies\:(13-6)\:m^{2}$

$\large{\underline{\boxed{\mathrm\purple{\implies\:7\:m^{2}}}}}$

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$\dag\:\underline{\sf Some\:Formula\:related\:to\:cuboid\::}$

• $\sf\:TSA=2(lb+bh+hl)$

• $\sf\:LSA=2(l+b)h$

• $\sf\:Volume=l \times b \times h$

• $\sf\:Diagonal= \sqrt{l^{2} \times b^{2} \times h^{2}}$

• $\sf\:Perimeter=4(l + b + h)$

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!! Hope it helps !!