A construction engineer designs a cone and a hemisphere, both of radius r, to be made from the same volume of concrete. If the volumes are equal, what is the height of the cone in terms of r?
Show answer & explanation
Correct answer: B
Explanation
Given:
Radius of the cone = r
Radius of the hemisphere = r
Both have equal volumes.
By the formula:
Volume of the hemisphere = (2/3)πr³
Volume of the cone = (1/3)πr²h
(1/3)πr²h = (2/3)πr³
r²h = 2r³
h = 2r³ / r²
h = 2r