Question

Two cubes each of volume 64 cm^3 are joined end to end. Find the surface are and volume of the resulting cuboid.​

Answer 1

Answer :-

• The surface area of resulting cuboid = 160cm².
• The volume of resulting cuboid = 128cm³.

Step-by-step explanation:

To Find:-

• The surface area and volume of resulting cuboid.

Solution:

Given that,

• Two cubes if volume, are joined end to end = 64cm³

∴ Side of a cube :-

⇒ a³ = 64 ... [ Volume of cube = (a)³ ]

⇒ a³ = 4 × 4 × 4

⇒ a = 4cm.

Therefore, The length, breadth and height, on joining two cubes,

⇒ Length = ( 4cm + 4cm ) = 8cm

⇒ Breadth = 4cm

⇒ Height = 4cm

According the question,

• The surface area of resulting cuboid :-

We know,

Total surface area of cuboid = 2 ( lb + bh + hl ) sq. units,

Where,

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

⇒ 2 ( lb + bh + hl )

⇒ 2 ( 8*4 + 4*4 + 8*4 )

⇒ 2 ( 32 + 16 + 26)

⇒ 2 ( 80 )

⇒ 2*80

⇒ 160cm²

• The volume of resulting cuboid :-

We know,

Volume of cuboid = ( l × b × h ) cubic units,

Where,

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

⇒ ( l × b × h )

⇒ ( 8 × 4 × 4 )

⇒ ( 32 × 4 )

⇒ 128cm³

Answer 2

Given :

• Two cubes each of volume 64 cm³ are joined end to end.

To find :

Find the surface are and volume of the resulting cuboid.

Solution :

Let us ,

The volume of cube 64cm³

Now ,

$\sf Side \: of \: cube = \sqrt[3]{64} = 4cm$

Will be,

$\sf Length \: of \: resulting \: cuboid = 4 + 4 = 8$

let Now,

$\sf Surface \: area \\ \sf = 2(lb + hl + bh) \\ \sf = 2(4(4) + 4(8) + 8(4) \\ \sf = 2(16 + 32 + 32) \\ = 2(80) = \sf \: \red{160cm {}^{2}}$