A cylindrical disc of thickness 1 cm is made by melting two solid cylinders of radii 4 cm and 5 cm, and length 6 cm and 4 cm, respectively. The radius of the new cylinder is:
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Correct answer: D
Explanation
The correct answer is option 4 i.e. 14 cm.
Radius(r1) = 4 cm and Height (h1) = 6 cm
V1 = πr12h1 = π(4)2 × 6 = π × 16 × 6 = 96π cm3
Radius (r2) = 5 cm and Height (h2) = 4 cm
V2 = πr22h2 = π(5)2 × 4 = π × 25 × 4 = 100π cm3
Total Volume = V1 + V2 = 96π + 100π = 196π cm3
Let the radius = R and Thickness (height) = 1 cm
⇒ πR21 = 196π ⇒ R2 = 196 ⇒ R = = 14 cm