Two hemispheres of radii 2 cm and 4 cm, respectively, are melted and recast into another hemisphere. What is the approximate total surface area of the newly formed hemisphere?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 163 cm2.
Volume of hemisphere = (2/3)πr3
Volume of first hemisphere = (2/3)π × 8 = 16π/3 cm3
Volume of second hemisphere = (2/3)π × 64 = 128π/3 cm3
Total volume = 16π/3 + 128π/3 = 144π/3 = 48π cm3
Let the radius of new hemisphere = R cm
For new hemisphere: (2/3)πR3 = 48π
⇒ R3 = 72
⇒ R ≈ 4.16 cm
Total surface area of hemisphere = 3πr2 = 3 × 22/7 × 4.162 ≈ 163 cm2