Question

Two cubes each of volume 27^3cm are joined end to end to form a solid. Find the surface area. of resulting solid.​

Answer 1

Given :-

• Two cubes each of volume 27cm³ are joined to make a cuboid .

To Find :-

• The surface area of the resulting solid .

Solution :-

Given that the volume of cube is 27cm³ . We know that the volume of cube is given by (side)³ .

So , if we assume each side to be a , then ,

$\longrightarrow$ a³ = 27cm³

$\longrightarrow$ a = ³√{27cm³}

$\longrightarrow$ a = ³√3³cm³

$\longrightarrow$ a = 3 cm .

• Hence , if we join two cubes we will get a cuboid of length 3cm + 3cm = 6cm . (l)
• The breadth would be 3cm .( b)
• The height would be 3cm .(h)

See attachment for figure .

And as we know that TSA of cuboid is ,

$\longrightarrow$TSA = 2( lb + bh + hl )

$\longrightarrow$ TSA = 2 ( 6*3 + 3*3 + 3*6) cm²

$\longrightarrow$TSA = 2 ( 18 +9 +18 )cm²

$\longrightarrow$ TSA = 2 * 45cm²

$\longrightarrow$ TSA = 90 cm²

Hence the new surface area of the solid is 90cm² .

I hope this helps.