The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm3, then what is the slant height of the cone? (Use π = 3.14)
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 13 cm.
Given that
The ratio of radius and height of a circular cone = 5 : 12
Its volume is 314 cm3,
Formula used
Volume of a cone = ⅓ 𝜋r2h cubic units
Slant height (l) = √(r2 + h2)
Calculation
⇒ ⅓ 𝜋r2h = 314
⇒ ⅓ × 3.14 × 25x2 × 12x = 314
⇒ 100x3 = 100
⇒ x3 = 1
⇒ x = 1
The radius (r) = 5 cm and height (h) = 12 cm
Hence, Slant height (l) = √(52 + 122) = √(25 + 144) = √169 = 13 cm