Find the volume of a cone of radius 3.5cm and vertical height 12cm. [Take π = 22/7]

Analyze the question: We need the volume of a cone with radius r = 3.5 cm and vertical height h = 12 cm, using π = 22/7.

Concept: The volume of a cone is one-third the volume of a cylinder with the same base and height:

V = (1/3)πr²h

Solution:

1. Substitute the values: V = (1/3) × (22/7) × (3.5)² × 12

2. Calculate r²: (3.5)² = 12.25

3. The 12 and the 1/3 combine nicely: (1/3) × 12 = 4 V = (22/7) × 12.25 × 4

4. Simplify (22/7) × 12.25: 12.25 ÷ 7 = 1.75, and 1.75 × 22 = 38.5

5. Multiply by 4: V = 38.5 × 4 = 154 cm³

Tip: When the radius is 3.5 (which is 7/2), the 7 in π = 22/7 cancels nicely. Write r = 7/2, so r² = 49/4. Then V = (1/3)(22/7)(49/4)(12) = 154. Look for such cancellations to save time in the exam. Also, always remember the 1/3 for cones, since forgetting it would give 462 cm³, which is a common trap.