NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.3

Question 1

Step 1: Write the formula for the volume of a cube.
Volume of a cube = (edge)³.

Step 2: Find the volume of each cube.

• Cube with edge 3 cm: Volume = (3^3 = 27 , ext{cm}^3)
• Cube with edge 4 cm: Volume = (4^3 = 64 , ext{cm}^3)
• Cube with edge 5 cm: Volume = (5^3 = 125 , ext{cm}^3)

Step 3: Add all the volumes to get the total volume of metal.
Total volume = (27 + 64 + 125 = 216 , ext{cm}^3).

Step 4: This total volume is used to make one new cube.
Let the edge of the new cube be (a).

Step 5: Volume of new cube = (a^3).
So, (a^3 = 216).

Step 6: Find cube root of 216.
(a = sqrt[3]{216} = 6 , ext{cm}).

Final Answer: The edge of the new cube is 6 cm.