NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 12: Surface Areas & Volumes - Exercise 12.1

Question 12

Step 1: Write the given values.

• Base diameter of cylinder = 2 cm
• So, radius of cylinder \(r = \tfrac{2}{2} = 1\,\text{cm}\)
• Height of cylinder \(h = 16\,\text{cm}\)
• Number of spheres formed = 12

Step 2: Find the volume of the cylinder.

Formula: \(V_{\text{cylinder}} = \pi r^2 h\)

\(= \pi (1)^2 (16) = 16\pi\,\text{cm}^3\)

Step 3: Let the radius of each sphere be \(R\).

Volume of one sphere: \(V_{\text{sphere}} = \tfrac{4}{3}\pi R^3\)

Volume of 12 spheres: \(12 \times \tfrac{4}{3}\pi R^3\)

Step 4: Since the metal is melted, total volume remains the same.

So, \(16\pi = 12 \times \tfrac{4}{3}\pi R^3\)

Step 5: Cancel \(\pi\) from both sides.

\(16 = 16R^3\)

Step 6: Solve for \(R^3\).

\(R^3 = 1 \;\Rightarrow R = 1\,\text{cm}\)

Step 7: Find the diameter of each sphere.

Diameter = \(2R = 2 \times 1 = 2\,\text{cm}\)

Final Answer: Diameter of each sphere is 2 cm.