Question

Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. the edge of the new cube formed is

Answer 1

volume of first cube= 6×6×6cu.cm
=216 cu. cm

volume of second cube=8×8×8cu.cm
=512cu.cm

volume of third cube= 10×10×10 cu.cm
= 1000 cu. cm


sum of volumes of all cubes = volume of the biggest cube.

216+512+1,000 cu. cm=side ^ 3

=1,728cu. cm=side ^ 3

side= 12 cm.

Answer 2

Given :-

• Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube$.$

To find :-

• What is the edge of the new cube formed ?

Solution :-

Let the edge of the new cube x cm.

Then, as per the question

⇒ x³ = [ ( 6 )³+ ( 8 )³+ ( 10 )³ ] cm³

⇒ x³ = ( 216 + 512 + 1000 ) cm³

⇒ x³ = 1728 cm³

⇒ x³ = ( 2³ × 6³ ) cm

⇒ x = 3√ ( 2 × 6 )³ cm

⇒ 2 × 6 cm

⇒ 12 cm

hence, the edge of the new cube formed is 12 cm .

______________________

Some important formulas :-

• Volume of cone ↠1/3 πr²h
• Volume of sphere ↠4/3 πR³
• Volume of cube ↠ (Side)³
• Volume of cylinder ↠ πr²h
• Volume of Cone ↠ ⅓ × πr²h
• T.S.A of Cube ↠ 6 × (Side)²
• T.S.A of Cylinder ↠ 2πr² + 2πrh
• L.S.A of Cube ↠ 4 × (Side)²
• L.S.A of Cylinder ↠ 2πrh
• L.S.A of Cone ↠ πrl

_______________________