Question

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2cubes of volume 64cm^3 are joined end to end. Find the surface area of the resulting cuboid.

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Answer 1

Correction in Question-

2 cubes each of volume 64cm^3 are joined end to end. Find the surface area of the resulting cuboid.

Given-

• Volume of 2 cubes each is 64 cm³

To find-

• Side of each cubes
• Surface area of cuboid

Formula to be used-

• Volume of a cube = a³
• S.I.A of Cuboid = 2(LB + LH + BH)

Step-by-step solution-

(i.) Vol. of cube = a³

64 cm³ = a³

a³ = 4³

a = 4

hence,side of each cube is 4 cm

(ii.) Now,

• Length of cuboid= side of cube+side of cube = 4 + 4 = 8 cm
• Breadth of cuboid= side .i.e 4 cm
• Height of cuboid= side .i.e 4 cm

(iii) Surface area of cuboid = 2(LB + LH + BH)

S.I.A = 2(8*4 + 8*4 + 4*4)

S.I.A = 2(32 + 32 + 16)

S.I.A = 2*80

S.I.A = 160

hence, surface area of cuboid is 160 cm²

Answer 2

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Let the length of each edge of the cube of volume 64cm^3 be x cm.

then, volume =64cm^3

⇒x^3 =4^3 ⇒x=4cm

The dimensions of the cuboid so formed are

Length=L=(4+4)=8cm

Breadth=b=4cm

Height=h=4cm

Surface area of the cuboid=2(8×4+4×4+8×4)cm^2

=160cm^2

Volume of the cuboid=lbh=8×4×4cm^3 =128cm^3

HOPE IT HELPS