Question

Find the total surface
area and length of the
diagonal of a cuboid whose measures are
= 12cm, b=4cm, h=3cm​

Answer 1

Answer:

Surface Area of Cuboid = 41,472 $cm^{2}$

Diagonal = 13cm

Step-by-step explanation:

l = 12cm

b = 4cm

h = 3cm

Total Surface Area of Cuboid = 2 (lb + bh + hl)

= 2 (12×4 + 4×3 + 3×12)

= 2 × 48 × 12 × 36

= 41,472 $cm^{2}$

Diagonal of cuboid = $\sqrt{ l^{2} + b^{2} + h^{2}$

= $\sqrt{12^{2} + 4^{2} + 3^{2} }$

=$\sqrt{169}$

= 13cm

Answer 2

Answer :-

• The total surface of cuboid is 192cm².
• The diagonal of cuboid is 13cm.

Step-by-step explanation:

To Find :-

• The total surface area of cuboid
• The length of diagonal of cuboid

Solution:

Given that,

• Length of cuboid = 12cm
• Breadth of cuboid = 4cm
• Height of cuboid = 3cm

Therefore,

• The total surface area of cuboid.

As we know that,

$\boxed{\sf{\purple{Total \: surface \: area \: of \: cuboid = 2 ( lb + bh + hl )}}}$

Where,

• l = Length
• b = Breadth
• h = Height

$\sf{= 2 ( lb + bh + hl )} \\ \\ \sf{= 2 ( 12 \times 4 + 4 \times 3 + 3 \times 12 )} \\ \\ \sf{= 2 ( 48 + bh + hl )} \\ \\ \sf{= 2 ( 48 + 12 + hl )} \\ \\ \sf{= 2 ( 48 + 12 + 36 )} \\ \\ \sf{= 2 ( 60 + 36 )} \\ \\ \sf{= 2 ( 96 )} \\ \\ \sf{= 2 \times 96} \\ \\ \sf{ = \purple{192} \: \bigstar}$

Hence,

• The total surface of cuboid is 192cm².

Now,

• The length of diagonal of cuboid.

As we know that,

$\boxed{\sf{\purple{Diagonal \: of \: cuboid = \sqrt{{l}^{2} + {b}^{2} + {h}^{2}}}}}$

Where,

• l = Length
• b = Breadth
• h = Height

$\sf{ = \sqrt{{l}^{2} + {b}^{2} + {h}^{2}}} \\ \\ \sf{ = \sqrt{{12}^{2} + {4}^{2} + {3}^{2}}} \\ \\ \sf{ = \sqrt{144 + {4}^{2} + {3}^{2}}} \\ \\ \sf{ = \sqrt{144 + 16 + {3}^{2}}} \\ \\ \sf{ = \sqrt{144 + 16 + 9}} \\ \\ \sf{ = \sqrt{144 + 25}} \\ \\ \sf{ = \sqrt{169}} \\ \\ \sf{= \purple{13} \: \bigstar}$

Hence,

• The diagonal of cuboid is 13cm.