An ice cream is in the form of a cone surmounted by a hemisphere. If the base radius of the cone is 3.5 cm and the height of the ice cream is 10 cm, then find the volume of the ice cream (in cm³).
$$(\pi = \frac{22}{7})$$

Question

An ice cream is in the form of a cone surmounted by a hemisphere. If the base radius of the cone is 3.5 cm and the height of the ice cream is 10 cm, then find the volume of the ice cream (in cm³).  
$$(\pi = \frac{22}{7})$$

Accepted Answer

1. **Understand the structure**:  
   The ice cream consists of a cone and a hemisphere.  
   - Radius of both cone and hemisphere = $$ r = 3.5 \, 	ext{cm} $$.  
   - Total height = $$ 10 \, 	ext{cm} $$.  
   - Height of cone = Total height - Radius of hemisphere = $$ 10 - 3.5 = 6.5 \, 	ext{cm} $$.

2. **Formula for total volume**:  
   Total volume = Volume of cone + Volume of hemisphere.  
   - Volume of cone = $$ \frac{1}{3} \pi r^2 h $$.  
   - Volume of hemisphere = $$ \frac{2}{3} \pi r^3 $$.

3. **Combine and simplify**:  
   Total volume = $$ \frac{1}{3} \pi r^2 (h + 2r) $$.

4. **Substitute values**:  
   Using $$ r = 3.5 $$, $$ h = 6.5 $$, and $$ \pi = \frac{22}{7} $$:  
   $$
   V = \frac{1}{3} \cdot \frac{22}{7} \cdot (3.5)^2 (6.5 + 7)
   $$  
   $$
   V = \frac{1}{3} \cdot \frac{22}{7} \cdot 12.25 \cdot 13.5
   $$  
   $$
   V = \frac{1}{3} \cdot 22 \cdot 12.25 \cdot 1.92857
   $$  
   $$
   V = 173.25 \, 	ext{cm}^3.
   $$

Thus, the volume of the ice cream is **173.25 cm³**, and the correct answer is **(c)**.

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