Question

find the side of the new cube if three cubes of iron whose edges are 6 cm 8cm and 10 cm respectively are method and formed into a singal cube ​

Answer 1

Answer:

Edge of the first cube = 6 cm

Volume of the first cube = (side)³ = (6)³ cm³ Edge of the second cube = 8 cm

Volume of the secondcube=(side)³ =(6)³cm³

Edge of the third cube = 10 cm

Volume of the third cube = (side)³ = (10)³ cm³.

Let “a” be side edge of the new formed cube.

Volume of the formed cube = Volume of the First cube + Volume of the Second cube + Volume of the Third Cube.

a³ = 63 + 83 + 103

= 216 + 512 + 1000

= 1728 0r

a = 12

• Therefore , Edge of the new cube is 12 cm.

Answer 2

Correct question,

Find the side of the new cube if three cubes of iron whose edges are 6 cm 8cm and 10 cm respectively are melted and formed into a single cube

SOLUTION:

Given:

The side of the cubes are given,

• First cube's side = 6 cm
• Second cube's side = 8 cm
• Third cube's side = 10 cm

To find:

The side of the new cube formed by melting the three cubes.

• As the three cubes are melted to form a new cube, so the volume of the new cube will be equal to the volume of the three cubes.

⇒ The volume of new cube = Sum of volumes of three cubes

⇒ (SIDE)³ = (side)³ + (side)³ + (side)³

⇒ (SIDE)³ = 6³ + 8³ + 10³

⇒ (SIDE)³ = 216 + 512 + 1000

⇒ (SIDE)³ = 1728

$\implies SIDE = \sqrt[3]{1728}$

∴ SIDE = 12 cm

Hence,

• The side of the newly formed cube by melting the three cubes is 12 cm.