Question

Three metal cubes of sides 6 cm, 8 cm and 10 cm are melted and recast into a big cube. Find its total surface area..​

Answer 1

$\sf{\huge{\underline{\green{Given :-}}}}$

• Three cubes of metal whose edges are 6 cm, 8 cm and 10cm respectively are melted to form a big cube.

$\sf{\huge{\underline{\green{To\:Find :-}}}}$

• The total surface area of the new cube .

$\sf{\huge{\underline{\green{Answer :-}}}}$

According to the question,

Three cubes of metal whose edges are 5 cm, 8 cm and 10cm are melted to form a single cube.

First cube of edge = 6 cm

The volume of the cube = a³

➝ a × a × a

➝ 6 × 6 × 6

➝ 36 × 6

➝ 216 cm³

Second cube of edge = 8 cm

The volume of the cube = a³

➝ a × a × a

➝ 8 × 8 × 8

➝ 64 × 8

➝ 512 cm³

Third cube of edge = 10 cm

The volume of the cube = a³

➝ a × a × a

➝ 10 × 10 × 10

➝ 100 × 10

➝ 1000 cm³

The volume of the Big cube form by combining the three cubes = Vol of cube 1 + Vol of cube 2 + Vol of cube 3

➝ 216 + 512 + 1000

➝ 728 + 1000

➝ 1728 cm³

The volume of the new cube is 1728 .

We know that, The volume of the cube is a³.

➝ a³ = 1728

➝ a = $\sqrt[3]{1728}$

➝ a = 12 cm

The edge of the new cube is 12 cm .

TSA of cube = 6a²

➝ 6 × 12 × 12

➝ 6 × 144

➝ 864 cm²

______________________________________

Answer 2

Given:-

• $Edge\:of\:Cube_1\:= \: 6cm.$

• $Edge\:of\:Cube_2\:= \: 8cm.$

• $Edge\:of\:Cube_3\:= \: 10cm.$

To Find:-

• Total Surface Area of new cube formed

Formula used:-

• Volume of Cube = Side³ or a³

• Total Surface Area of Cube = 6×Side² or 6a²

Solution:-

⟾ Sum of volume of three cubes

= $(a_1)³+(a_2)³+(a_3)³$

= $(6)³+(8)³+(10)³$

= $216+512+1000$

= $1728\:cm³$

On melting the three cubes a new cube is formed with edge a'.

Volume of new cube = Sum of Volumes of three cubes

⟾ $a'³ = 1728$

⟾ $a' = \sqrt[3]{1728}$

⟾ $a' = 12 cm$

Total Surface Area of New Cube

= 6a'²

= 6(12)²

= 864 cm²

Hence, the total Surface Area of New Cube is 864 cm².

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