The slant height of a cone is 5cm and the radius of its base is 3cm. Find, correct to the nearest whole…

Analyze the question: We're given the slant height (l = 5 cm) and the base radius (r = 3 cm). To find the volume we need the vertical height h, which we get from the right-angled triangle formed by h, r and l.

Concept:

• Pythagoras: l² = r² + h²
• Volume of a cone: V = ⅓πr²h

Solution:

Step 1: Find the height. h² = l² − r² = 5² − 3² = 25 − 9 = 16 h = 4 cm (the 3-4-5 triangle)

Step 2: Find the volume. V = ⅓ × (22/7) × 3² × 4 V = ⅓ × (22/7) × 9 × 4 V = (22 × 36) / (3 × 7) V = 792 / 21 V = 37.71 cm³

Step 3: Round to the nearest whole number. V ≈ 38 cm³

Option A (48 cm³) is a common trap. It comes from forgetting the ⅓ and wrongly using the slant height, or from other slips. Option D (12 cm³) comes from using the wrong values or a wrong formula.

Tip: Whenever a cone question gives the slant height, find the vertical height first with Pythagoras. Watch for the 3-4-5 triplet, as it shows up often in WASSCE, JAMB and NECO. Also remember that the volume formula uses the vertical height h, not the slant height l.