Total surface area of a solid hemisphere is 4158 cm². It is melted to form…
2021
Total surface area of a solid hemisphere is 4158 cm². It is melted to form cylinders whose height is 1 cm and radius of base is 7 cm. How many cylinders will be formed?
- A.
126
- B.
156
- C.
96
- D.
136
Attempted by 4 students.
Show answer & explanation
Correct answer: A
Find the radius: Total Surface Area (TSA) of a hemisphere = 3 * pi * r^2.
3 * (22/7) * r^2 = 4158
r^2 = (4158 * 7) / (3 * 22) = 441
r = 21 cm.
Calculate volume of hemisphere: V = (2/3) * pi * r^3.
V = (2/3) * (22/7) * 21 * 21 * 21 = 19404 cm^3.
Calculate volume of one cylinder: V_cyl = pi * r^2 * h.
V_cyl = (22/7) * 7 * 7 * 1 = 154 cm^3.
Find number of cylinders: Total Volume / V_cyl = 19404 / 154 = 126.
Final Answer: Option 1 (126)