Question

4.
Three metal cubes with edges 15 cm., 12 cm. and 9 cm. respectively are melted together
and formed into a single cube. Find the diagonal of this cube.
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Answer 1

QUESTION:

• Three metal cubes with edges 15 cm., 12 cm. and 9 cm. respectively are melted together and formed into a single cube. Find the diagonal of this cube.

ANSWER:

• Diagonal of new cube formed = 31.17 cm

GIVEN:

• Three metal cubes with edges 15 cm., 12 cm. and 9 cm.

TO FIND:

• Diagonal of new cube formed

SOLUTION:

Formula

• Volume of cube = (Edge)³

Finding the volume of each cube seperately.

• Volume of 1st Cube = (15)³ = 3375 cm³
• Volume of 2nd Cube = (12)³ = 1728 cm³
• Volume of 3rd Cube = (9)³ = 729 cm³

Now; According to the question:

=> Volume of 1st Cube +Volume of 2nd Cube +Volume of 3rd Cube = Volume of New Cube

=> 3375 + 1728+ 729 = Volume of New Cube

=> 5832 cm³ = (Edge of new cube)³

=>( Edge of new cube)³ = (18 cm)³

=> Edge of new cube = 18 cm

Now Diagonal of Cube = √3 * Edge

= √3 * 18

= 31.17 cm ( Approx)

• Diagonal of new cube formed = 31.17 cm