Question

three cubes of metal with edges 3cm,4cm and 5cm respectively are melted to form a single cube. find the lateral surface area of the new cube formed?​

Answer 1

ANSWER :

Lateral surface area of the new cube is 144 cm².

EXPLANATION :

GIVEN :-

• Three cubes of metal with edges 3cm,4cm and 5cm respectively are melted to form a single cube.

TO FIND :-

• Lateral surface area of new cube.

SOLUTION :-

★Edge of 1st cube = 3 cm.

★Edge of 2nd cube = 4 cm.

★Edge of 3rd cube = 5 cm.

Volume of cube = (a)³[ a = edge]

✪Now find the volume of 1st , 2nd and 3rd cube.✪

★Volume of 1st cube = (3)³ =27cm³

★Volume of 2nd cube=(4)³=64cm³

★Volume of 3rd cube=(5)³=125cm³

Total volume of 3 cubes,

= (27+64+125) cm³

= 216 cm³

✪ 3 cubes are melted to form a single cube .✪

Let the edge of the new cube be A cm.

Volume of new cube = A³ cm³

According to the question,

$\sf{\:\:\:\:A^3=216}$

$\implies\sf{A^3=6^3}$

$\implies\sf{A = 6}$

Edge of the new cube = 6 cm.

${\boxed{\sf{Lateral\: surface\: area\: of\:cube=4\times\:edge^2}}}$

LSA of cube = 4 × 6² cm²

→LSA of cube = 144 cm²

Therefore the LSA of the new cube is 144 cm².

Answer 2

$\large{\underline{\red{\rm{AnswEr:144\:cm^2}}}}$

$\huge\bold\red{\underline{Solution:}}$

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

$\bold\orange{Three\: cubes\:of metal\:with\: edges}$

$\bold\green{Edge\:of\:1st\:cube=3cm}$

$\bold\purple{Edge\:of\:2nd\:cube=4cm}$

$\bold\orange{Edge\:of\:2nd\:cube=5cm}$

$\bold\purple{\boxed{Find:L.S.A\:of\:new\:cube}}$

$\bold\green{\underline{A.T.Q}}$

• Using formula to calculate Volume

$\bold\purple{\boxed{Volume\:of\:cube=Edge^3}}$

$\bold\orange{Volume\:of\:1st\:cube=3^3=27\:cm^3}$

$\bold\green{Volume\:of\:2nd\:cube=4^3=64\:cm^3}$

$\bold\purple{Volume\:of\:3rd\:cube=5^3=125\:cm^3}$

Three cubes are melted to form a single cube

$\bold\purple{\boxed{Sum\:of\: Volume\:3\: cubes=New\:cube}}$

$\bold\green{Volume\:of\:Cube=27+64+125}$

$\bold\red{Volume\:of\:Cube=216\:cm^3}$

$\bold\purple{\boxed{Side\:of\:new\:cube=New\: Volume}}$

$\bold\green{Side\:of\:new\:cube=cube\:216}$

$\bold\green{Side\:of\:new\:cube=6\:cm^3}$

Hence,

$\bold\purple{\boxed{L.S.A=4*side^2}}$

$\bold\orange{L.S.A=4*6^2}$

$\bold\pink{L.S.A=4*36}$

$\bold\green{L.S.A=144\:cm^2}$