Find the volume of a cone which has a base radius of 5 cm and slant height of 13 cm.

Analyze the question: We're given the base radius (r = 5 cm) and the slant height (l = 13 cm). The volume formula needs the perpendicular height (h), so we must find h first.

Concept:

• Volume of a cone: V = ⅓πr²h
• Slant height, radius and height form a right-angled triangle: l² = r² + h²

Solution:

Step 1: Find the height h² = l² − r² = 13² − 5² = 169 − 25 = 144 h = 12 cm (a 5-12-13 triple)

Step 2: Find the volume V = ⅓ × π × 5² × 12 V = ⅓ × π × 25 × 12 V = ⅓ × 300π V = 100π cm³

Tip: Memorize the common Pythagorean triples (3-4-5, 5-12-13, 8-15-17, 7-24-25). They save time in the exam. Also, don't use the slant height directly in the volume formula. A common trap is to compute ⅓π(25)(13) = 325π/3, which is option C, a distractor.