A metal hemisphere of radius 12.6 cm is melted to form a right circular cylinder. The ratio of the cylinder's curved surface area to total surface area is 1 : 2. Calculate the radius of the base of the cylinder. Use π = 22/7. (in approx)
Show answer & explanation
Correct answer: C
Explanation
Given:
Radius of the hemisphere = 12.6 cm
π = 22/7
According to the formulas:
Volume of the hemisphere = (2/3)πR³
Volume of the cylinder = πr²h
Curved Surface Area : Total Surface Area = 1 : 2
Curved Surface Area = 2πrh
Total Surface Area = 2πr(h + r)
(2πrh) / (2πr(h + r)) = 1/2
h / (h + r) = 1/2
2h = h + r
h = r
Now, we will equate the volumes:
(2/3)π(12.6)³ = πr²h
h = r
(2/3)π(12.6)³ = πr³
r³ = (2/3)(12.6)³
12.6³ = 2000.376
r³ = (2/3) × 2000.376
r³ = 1333.58
r = 11 cm