NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.3Question 1
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.3
Question. 1
Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.
Answer:
6 cm
Detailed Answer with Explanation:
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.