Two solid metallic right circular cones of heights 3.5 cm and 5.3 cm and base…
2022
Two solid metallic right circular cones of heights 3.5 cm and 5.3 cm and base radius of each cone 2.2 cm are melted and recast into a solid sphere. What is the surface area (in cm²) of the sphere?
- A.
9.68 π
- B.
14.52 π
- C.
19.36 π
- D.
29.04 π
Attempted by 2 students.
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Correct answer: C
Total volume of cones = (1/3)π(2.2)²(3.5 + 5.3). If the sphere radius is R, then (4/3)πR³ = (1/3)π(2.2)²(8.8), so R³ = (2.2)²(8.8)/4 = 10.648 = (2.2)³. Thus R = 2.2 cm and surface area = 4πR² = 19.36π cm².