The volume of a cone of height 3cm is 38$\frac{1}{2}$cm3. Find the radius of its base. [Take $\pi = \frac{22}{7}$]

Analyze the question: We are given a cone with height h = 3 cm and volume V = 38½ cm³ = 77/2 cm³. We need to find the base radius r, using π = 22/7.

Concept: The volume of a cone is

V = (1/3)πr²h

Solution:

1. Substitute the values: 77/2 = (1/3) × (22/7) × r² × 3

2. The 3's cancel: 77/2 = (22/7) r²

3. Make r² the subject: r² = (77/2) × (7/22)

4. Simplify: 77/22 = 7/2, so r² = (7/2) × (7/2) = 49/4

5. Take the square root: r = 7/2 = 3.5 cm

Answer: The radius is 3.5 cm, which is option B.

Check: V = (1/3)(22/7)(3.5²)(3) = (22/7)(12.25) = 38.5 cm³ ✓

Tip: When the height equals 3, the 1/3 cancels the h, so V = πr² directly. You only need r² = V ÷ π. Also, convert mixed numbers to improper fractions early (38½ = 77/2) so the 7 and 22 cancel neatly.