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

Question 9

Step 1: Identify the shape of the ice cream.

• The ice cream has two parts:
  • A hemisphere on the top.
  • A cone at the bottom.
• Radius of both = \(r = 5\,\text{cm}\).
• Height of cone = \(h = 10\,\text{cm}\).

Step 2: Volume of the hemisphere.

Formula for volume of hemisphere = \(\dfrac{2}{3}\pi r^3\).

Substitute values: \(\dfrac{2}{3}\pi (5^3) = \dfrac{2}{3}\pi (125) = \dfrac{250}{3}\pi\,\text{cm}^3\).

Step 3: Volume of the full cone.

Formula for volume of cone = \(\dfrac{1}{3}\pi r^2 h\).

Substitute values: \(\dfrac{1}{3}\pi (5^2)(10) = \dfrac{1}{3}\pi (25)(10) = \dfrac{250}{3}\pi\,\text{cm}^3\).

Step 4: Only \(\tfrac{5}{6}\) of the cone is filled.

So, filled cone volume = \(\dfrac{5}{6} \times \dfrac{250}{3}\pi = \dfrac{625}{9}\pi\,\text{cm}^3\).

Step 5: Total volume of ice cream.

Add hemisphere volume and filled cone volume:

\(\dfrac{250}{3}\pi + \dfrac{625}{9}\pi = \dfrac{750}{9}\pi + \dfrac{625}{9}\pi = \dfrac{1375}{9}\pi\,\text{cm}^3\).

Step 6: Approximate numerical value.

\(\dfrac{1375}{9}\pi \approx 480\,\text{cm}^3\).

Final Answer: The volume of the ice cream is about \(480\,\text{cm}^3\).