Question

how to solve the total surface area and the lateral surface area of a cuboid whose length is 12m,breadth is 9m and height is 7m​

Answer 1

Answer:

Total surface area of the cuboid is 510 m² and lateral surface area of the cuboid is 294 m².

Step-by-step explanation:

Given :-

• Length of cuboid = 12 m
• Breadth of cuboid = 9 m
• Height of cuboid = 7 m

To find :-

• Total surface area (TSA) and Lateral surface area (LSA) of cuboid.

Solution :-

Formula used :

• ${\boxed{\sf{TSA\:of\: cuboid=2(l\times\:b+b\times\:h+l\times\:h)}}}$

• ${\boxed{\sf{LSA\:of\: cuboid=2h(l+b)}}}$

Here,

• l = length
• b = breadth
• h = height

TSA of cuboid,

= 2(l×b+b×h+l×h)

= 2(12×9+9×7+12×7) m²

= 2(108+63+84) m²

= 2 × 255 m²

= 510 m²

Total surface area of cuboid is 510 m².

LSA of cuboid,

= 2h(l+b)

= 2×7 (12+9) m²

= 2×7×21 m²

= 294 m²

Lateral surface area of cuboid is 294 m².

__________________

Answer 2

Answer:

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\linethickness{0.4mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{12 m}}\put(4,6.3){\sf{9 m}}\put(11.2,7.5){\sf{7 m}}\end{picture}$

• Length ( L ) = 12 m
• Breadth ( B ) = 9 m
• Height ( H ) = 7 m

• Total Surface Area of Cuboid :

$:\implies\sf TSA=2(LB+BH+HL)\\\\\\:\implies\sf TSA = 2(12 \times 9 + 9 \times 7 + 7 \times 12)\\\\\\:\implies\sf TSA = 2(108 + 63 + 84)\\\\\\:\implies\sf TSA = 2 \times 255\\\\\\:\implies\underline{\boxed{\sf TSA = 510 \: {m}^{2} }}$

$\rule{180}{1}$

• Lateral Surface Area of Cuboid :

$:\implies\sf CSA=2(Length+Breadth) \times Height\\\\\\:\implies\sf CSA = 2(12 + 9) \times 7\\\\\\:\implies\sf CSA = 2 \times 21 \times 7\\\\\\:\implies\underline{\boxed{\sf CSA = 294 \:{m}^{2} }}$

⠀⠀⠀⠀$\rule{150}{2}$

$\boxed{\begin{minipage}{6 cm}\underline{\text{Formulae Related to Cuboid :}}\\ \\\sf CSA = 2(Length + Breadth)\times\:\sf Height\\\\\sf TSA=2(lb+bh+hl)\\ \\Volume=Length\times Breadth\times Height\\ \\Diagonal=\sqrt{l^2+b^2+h^2}\end{minipage}}$