Question

A cuboid has total surface area of 40m², and its lateral surface area is 26m². Find the area of its base.​

Answer 1

Given:- total surface area of cuboid is 40m² and lateral surface area is 26m².

To Find:- area of base of cuboid.

Solution :-

Lateral surface area of cuboid = 26m²

⇒ 2( l + b )h = 26m²

⇒ 2lh + 2bh = 26 ......eq(1)

Total surface area of cuboid = 40m²

⇒ 2( lb + bh + hl ) = 40m²

⇒ 2lb + 2bh + 2hl = 40

⇒ 2lb + 26 = 40 ......[from eq(1)]

⇒ 2lb = 40 - 26

⇒ 2lb = 14

⇒ lb = 14/7

⇒ l×b = 7m² .

As we know that the base of cuboid is of rectangular shape and area of rectangle is l×b(7m²).

Hence, the area of base is 7m².

Answer 2

$\large\underline{ \underline{ \sf \maltese{ \: Question:- }}}$

• A cuboid has total surface area of 40m², and its lateral surface area is 26m². Find the area of its base.

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

• Total Surface Area = 40m
• Lateral Surface area = 26m

$\large\underline{ \underline{ \sf \maltese{ \: To \: Find :- }}}$

• What is the Surface Area of Base ?

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

${:} \longrightarrow \sf{ \boxed{{\bf{ Total \: Surface \: Area \: = \: 2 \: ( Surface \: Area \: of \: base ) \: + \:} ( Lateral \: Surface \: Area )}}}$

$\qquad \quad {:} \longrightarrow \sf{{{\sf{ 40 \: = \: 2 \: ( Surface \: Area \: of \: base ) \: + \:} 26}}}$

$\qquad \quad {:} \longrightarrow \sf{{{\sf{ 40 \: - \: 26\: = \: 2 \: ( Surface \: Area \: of \: base ) }}}}$

$\qquad \quad {:} \longrightarrow \sf{{{\sf{ 14\: = \: 2 \: ( Surface \: Area \: of \: base ) }}}}$

$\qquad \quad {:} \longrightarrow \sf{{{\sf{ \cancel\frac{14}{2} \: = \: Surface \: Area \: of \: base }}}}$

$\qquad \quad {:} \longrightarrow \sf{{{\bf{ 7\: = \: \: Surface \: Area \: of \: base }}}}$

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$\begin{gathered}\begin{gathered}\qquad \therefore\: \sf{ Surface \: Area \: of \: base \: = \underline {\underline{7 {m}^{2} }}}\\\end{gathered}\end{gathered}$

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★ Additional Info :

• Volume of cylinder = πr²h
• T.S.A of cylinder = 2πrh + 2πr²
• Volume of cone = ⅓ πr²h
• C.S.A of cone = πrl
• T.S.A of cone = πrl + πr²
• Volume of cuboid = l × b × h
• C.S.A of cuboid = 2(l + b)h
• T.S.A of cuboid = 2(lb + bh + lh)
• C.S.A of cube = 4a²
• T.S.A of cube = 6a²
• Volume of cube = a³
• Volume of sphere = 4/3πr³
• Surface area of sphere = 4πr²
• Volume of hemisphere = ⅔ πr³
• C.S.A of hemisphere = 2πr²
• T.S.A of hemisphere = 3πr²

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