If the radius of the base and slant height of the cone is 6 cm and 10 cm, respectively, then the volume of the cone is equal to:
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 96π cm3.
Using the Pythagorean theorem to find the height (h) of the cone:
h² = slant height² - radius²
⇒ h² = 10² - 6²
⇒ h² = 100 - 36
⇒ h² = 64
⇒ h = √64
⇒ h = 8 cm
The volume (V) of a cone is given by the formula:
V = (1/3)πr²h
⇒ V = (1/3)π(6 cm)²(8 cm)
⇒ V = (1/3)π(36 cm²)(8 cm)
⇒ V = 96π cm³
Therefore, the volume of the cone is 96π cubic centimeters.