Question

Two cubes each of volume 64cm, are joined end to end together. Find total surface area of resulting cuboid.

Answer 1

Answer:

Given, volume of each cube is 64 cm³

⇒s³=64

⇒s=∛64

⇒s=4 cm.

When two cubes are joined , 

the length of the resulting cuboid(l) = side + side = 4+4 = 8 cm

its breadth(b) = side = 4cm

And its height(h) = side = 4cm

Total surface area of a cuboid = 2(lb+bh+hl)

⇒TSA=2[(8)(4)+(4)(4)+(4)(8)]

⇒TSA=2(32+16+32)

⇒TSA = 2(80)

⇒TSA = 160 cm²

∴ The surface area of the resulting cuboid is 160 cm².

Answer 2

AnswEr :

160 cm².

$\bf{\green{\underline{\underline{\bf{Given\::}}}}}$

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

$\bf{\green{\underline{\underline{\bf{To\:find\::}}}}}$

The total surface area of resulting cuboid.

$\bf{\green{\underline{\underline{\bf{Explanation\::}}}}}$

We know that the formula of the volume of cubes :

$\bf{\boxed{\sf{Volume\:of\:cube\:=\:Edge \times Edge\times Edge\: (a^{3} )}}}}$

$\mapsto\sf{Volume\:(V)=\:(a)^{3} }\\\\\\\mapsto\sf{64\:cm^{3}= (a)^{3} }\\\\\\\mapsto\sf{a=3\sqrt{64} }\\\\\\\mapsto\sf{\green{a=4\:cm}}$

Now,

Dimensions of the cuboid are :

$\bf{We\:have}\begin{cases}\sf{Length\:(l)=4\:cm}\\ \sf{Breadth\:(b)=4\:cm}\\ \sf{Height\:(h)=(4+4)cm=8cm}\end{cases}}$

Formula use :

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

$\leadsto\tt{T.S.A_{cuboid}=2(lb+bh+lh)\:\:sq.unit}\\\\\\\leadsto\tt{T.S.A_{cuboid}=2\big[(4\times 4 )+(4\times 8)+(4\times 8)\big]cm^{2} }\\\\\\\leadsto\tt{T.S.A_{cuboid}=2(16+32+32)\:cm^{2} }\\\\\\\leadsto\tt{T.S.A_{cuboid}=2(80)\:cm^{2} }\\\\\\\leadsto\tt{\green{T.S.A_{cuboid}=160\:cm^{2} }}$

Thus,

Total surface area of resulting cuboid is 160 cm² .