Three cubes whose edges measure 3cm,4cm,5cm respectively to form a single cube.Find its edge.Also find the surface area of the new cube.

Volume of new cube = Sum of volume of three cubes

= 3^{3} + 4^{3} + 5^{3 }

= 216 cm^{3}

i.e., (edge)^{3} = 216 cm^{3}

So, Edge of the single cube = 6 cm

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Given : Three cubes of metal with edges 3 cm, 4 cm and 5 cm are melted to form a new single cube

Let the edge of new cube be a.

⇒ Volume of new cube = Volumes of three small cubes

⇒ *a* ^{3} = (3 cm)^{3} + (4 cm)^{3} + (5 cm)^{3}

= a^{3} = 27 cm^{3} + 64 cm^{3} + 125 cm^{3}

= a^{3} = 216 cm^{3}

⇒ *a* = 6 cm

Hence Lateral surface area of new cube = 6*a* ^{2}

= 6 x (6 cm)^{2} = 6 x 36 cm^{2}

= 216 cm^{2}

- 2

Given : Three cubes of metal with edges 3 cm, 4 cm and 5 cm are melted to form a new single cube

Let the edge of new cube be a.

⇒ Volume of new cube = Volumes of three small cubes

⇒ *a* ^{3} = (3 cm)^{3} + (4 cm)^{3} + (5 cm)^{3}

= a^{3} = 27 cm^{3} + 64 cm^{3} + 125 cm^{3}

= a^{3} = 216 cm^{3}

⇒ *a* = 6 cm

Hence Lateral surface area of new cube = 6*a* ^{2}

- 3

Second edge= 4 cm

Third

^{ }edge = 5 cm

__VOLUME OF NEW CUBE = SUM OF VOLUME OF ALL THREE CUBES__

VOLUME = A

^{3}

V

_{1}= 3

^{3 }

V

_{2}=4

^{3}

V

_{3}=5

^{3}

V

_{1}+V

_{2}+V

_{3}=VOLUME OF NEW CUBE

27+64+125= 216cm

^{3}

Side of new cube = root of 216 (AS VOLUME = A

^{3})

Side = 6 cm

EDGE = 6cm

TSA = 6a

^{2}

= 6*(6)

^{2}

= 6*36

= 216 cm

^{2}

TOTAL SURFACE AREA = 216 CM

^{2 }EDGE = 6 CM

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- 4

To form a single large cube,

The total volume of all small cubes= 3

^{3}+4

^{3}+5

^{3}=27+64+125=216 cm3

So the edge of the larger cube is= 216

^{1/3}=6 cm

The total surface area of the larger cube is=6x

^{2}=6*36=216 cm

^{2}

Hence, the larger cube has a surface area of

__216 cm__

^{2}- 3

a^3 + b^3 + c^3 = x^3 .........( where x is edge of greater cube and a,b,c are edge of smaller cube)

3^3 + 4^3 + 5^3 = x^3

9+64+125 = x^3

216 = x^3

(6)^3 = x^3

on comparing x will equal to 6

so, edge of greater cube is equal to 6

Surface Area will equal to 6a^2

6 x (6)^2

216 cm^2

- 0

Volume of 1st cube = edge^3

=3^3

=27cm^3

Edge of 2nd cube=4cm

Volume of 2nd cube =4^3

=64cm^3

Edge of 3rd cube =5cm

Volume of 3rd cube =5^3

=125cm^3

Total volume of the 3 cubes =Volume of new cube

Volume of new cube = 27 +64+125cm^3

=216cm^3

Edge^3=216

Edge=6cm

Surface area of the new cube = 6×edge^2

=6×6^2

=216cm^2

- 1