Question

3. Three cubes of side 8cm are joined end to end. Find the surface area and volume of the resulting figure.

Answer 1

$\sf\huge\blue{\underline{\underline{ Question : }}}$

Three cubes of side 8cm are joined end to end. Find the surface area and volume of the resulting figure.

$\sf\huge\blue{\underline{\underline{ Solution : }}}$

★ Given that,

• Three cubes of side 8cm are joined end to end.

➡ On joining the three cube, it will be converted into cuboid shape.

• $\tt\red{:\implies Length_{(Cuboid)} = 8 + 8 + 8 = 24 cm. }$
• $\tt\red{:\implies Breadth_{(Cuboid)} = 8 cm. }$
• $\tt\red{:\implies Height_{(Cuboid)} = 8 cm. }$

★ To find,

• $\rm\blue{:\implies Total\:Surface\:area_{(Cuboid)} }$
• $\rm\blue{:\implies Volume_{(Cuboid)} }$

★ Now,

$\bf\: Total \:surface\: area_{(Cuboid)} = 2[lb + bh + lh]$

• Substitute the values.

$\bf\:\leadsto 2[ (24 \times 8) + (8 \times 8) + ( 24 \times 8)]$

$\bf\:\leadsto 2[192 + 64 + 192 ]$

$\bf\:\leadsto 2[448 ]$

$\bf\:\leadsto 896$

$\underline{\boxed{\sf{\purple{ \therefore Total\:surface\:area_{(Cuboid)} = 896 cm^{3}.}}}}\:\orange{\bigstar}$

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$\bf\:Volume_{(Cuboid)} = lbh$

$\bf\:\leadsto 24\times8\times8$

$\bf\:\leadsto 1536$

$\underline{\boxed{\bf{\purple{ \therefore Volume_{(Cuboid)} = 1536 cm^{3}}}}}\:\orange{\bigstar}$

______________________________________________________

Answer 2

figure:-

Given:-

• Three cubes of side 8cm and joined end to end.

To find:-

• Find total surface area of cuboid.?

Solutions:-

The dimensions of the resulting cuboid are:-

Length = 8 + 8 + 8 = 24cm

Breadth = 8cm

Height = 8cm

We know that;

• Total surface area of the cuboid = 2(lb + bl + lh)

=> 2(24 × 8 + 8 × 8 + 8 × 24)

=> 2(192 + 64 + 192)

=> 2(448)

=> 896cm²

• Total surface area of the cuboid = 896cm².

Hence, Total surface area of the cuboid is 896cm².

Some Important:-

• Total Surface area = 2 (Length x Breadth + breadth x height + Length x height)

• Surface area = 2 height(length + breadth)

• Volume of the cuboid = (length × breadth × height)

• Diagonal of the cuboid =√( l2 + b2 +h2)

• Perimeter of cuboid = 4 (length + breadth + height)