The volume of a right circular cone is 150π cm3 and its height is 18 cm. Find its slant height (in cm) (correct to 2 decimal places).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 18.68.
We know the volume of a right circular cone is given by the formula:
Volume = (1/3)πr²h
where:
r is the radius of the base
h is the height
We are given:
Volume = 150π cm³
Height (h) = 18 cm
Substituting the values:
⇒ 150π = (1/3)πr²(18)
Simplifying:
⇒ 150 = 6r²
Dividing both sides by 6:
⇒ 25 = r²
Taking the square root of both sides:
⇒ r = 5 cm
Now, to find the slant height (l), we can use the Pythagorean theorem, as the height, radius, and slant height form a right-angled triangle:
⇒ l² = r² + h² l² = 5² + 18² l² = 25 + 324 l² = 349
Taking the square root of both sides:
⇒ l ≈ 18.68 cm (rounded to 2 decimal places)
Therefore, the slant height of the cone is approximately 18.68 cm.